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Idealised system for theoretical analysis
A dynamical billiard is a dynamical system in which a particle alternates between free motion (typically as a straight line) and specular reflections
Dynamical_billiards
Type of dynamical system in mathematics
Outer billiards is a dynamical system based on a convex shape in the plane. Classically, this system is defined for the Euclidean plane, but one can also
Outer_billiards
Chaotic dynamical system, a type of "billiards"
Hadamard dynamical system (also called Hadamard's billiard or the Hadamard–Gutzwiller model) is a chaotic dynamical system, a type of dynamical billiards. Introduced
Hadamard's_dynamical_system
Dynamical system involving reflection
triangle have a periodic billiards path? More unsolved problems in mathematics In mathematics, triangular billiards is a dynamical system that models the
Triangular_billiards
Ball used in cue sports
billiard ball is a small, hard ball used in cue sports, such as carom billiards, pool, and snooker. The number, type, diameter, color, and pattern of
Billiard_ball
Mathematical model of the time dependence of a point in space
affect the evolution of the state variables. The study of dynamical systems is the focus of dynamical systems theory, which has applications to a wide variety
Dynamical_system
Geometrical GCD and LCM algorithm
This is a simple example of trajectory analysis used in dynamical billiards. Arithmetic billiards can be used to show how two numbers interact. Drawing
Arithmetic_billiards
Topics referred to by the same term
(called quadrillion in the short scale generally used in English) Dynamical billiards, the mathematical theory of particle trajectories within a closed
Billiard
Field of mathematics and science based on non-linear systems and initial conditions
Cliodynamics Coupled map lattice Double pendulum Duffing equation Dynamical billiards Economic bubble Gaspard-Rice system Logistic map Hénon map Horseshoe
Chaos_theory
Result in quantum chaos
mirage is a peculiar result in quantum chaos. Every system of quantum dynamical billiards will exhibit an effect called scarring, where the quantum probability
Quantum_mirage
Dynamical system governed by Hamilton's equations
A Hamiltonian system is a dynamical system governed by Hamilton's equations. In physics, this dynamical system describes the evolution of a physical system
Hamiltonian_system
Non-linear generalization of a Hilbert space
Burago and Serge Ferleger used CAT(0) geometry to solve a problem in dynamical billiards: in a gas of hard balls, is there a uniform bound on the number of
Hadamard_space
Dynamical system
The Fermi–Ulam model (FUM) is a dynamical system that was introduced by Polish mathematician Stanislaw Ulam in 1961. FUM is a variant of Enrico Fermi's
Fermi–Ulam_model
Geometric shape of rectangle and two semicircles
r^{2}+2ra=r(\pi r+2a)} . When this shape is used in the study of dynamical billiards, it is called the Bunimovich stadium. Leonid Bunimovich used this
Stadium_(geometry)
Feature of systems that defy description
equal, as is done for the notion of entropy in statistical mechanics. In dynamical systems, statistical complexity measures the size of the minimum program
Complexity
Mathematical study of illumination of rooms with mirrored walls
2140/gt.2016.20.1737. Wolecki, Amit (2019). "Illumination in rational billiards". arXiv:1905.09358 [math.DS]. "The Illumination Problem – Numberphile"
Illumination_problem
Type of a dynamical billiard first studied by Emil Artin in 1924
In mathematics and physics, the Artin billiard is a type of a dynamical billiard first studied by Emil Artin in 1924. It describes the geodesic motion
Artin_billiard
in a classically chaotic system correlating like that would be Sinai billiards:[further explanation needed] Energy levels: − ℏ 2 2 m ▽ 2 ψ + V ( x )
BGS_conjecture
Russian–American mathematician (born 1935)
work on dynamical systems. He contributed to the modern metric theory of dynamical systems and connected the world of deterministic (dynamical) systems
Yakov_Sinai
Theory in physics and mathematics
case of conservative systems are the measure-preserving dynamical systems. Informally, dynamical systems describe the time evolution of the phase space
Conservative_system
Property of measure-preserving dynamical systems
systems are difficult. Important mathematical examples come from dynamical billiards, where idealized particle collisions provide systems for which ergodicity
Ergodicity
English-language terms used in the three overarching cue sports disciplines: carom billiards referring to the various carom games played on a billiard table without
Glossary_of_cue_sports_terms
Laws in physics about force and motion
Noteworthy examples include the three-body problem, the double pendulum, dynamical billiards, and the Fermi–Pasta–Ulam–Tsingou problem. Newton's laws can be applied
Newton's_laws_of_motion
Form of pocket billiards popular in Eastern Europe
Russian pyramid, also known as Russian billiards (Russian: ру́сский билья́рд, russky bilyard), is a form of billiards played on a large billiard table with
Russian_pyramid
Soviet and American mathematician
The most famous class of chaotic dynamical systems of this type, dynamical billiards are focusing chaotic billiards such as the Bunimovich stadium ("Bunimovich
Leonid_Bunimovich
Shortest paths on a bounded deformed sphere-like quadric surface
limit c → 0, geodesics on a triaxial ellipsoid reduce to a case of dynamical billiards; extensions to an arbitrary number of dimensions (Knörrer 1980);
Geodesics_on_an_ellipsoid
Mathematical model which approximates the behavior of real gases
which describes the deviation of a real gas from ideal gas behavior Dynamical billiards – Idealised system for theoretical analysis – billiard balls as a
Ideal_gas
Subject of study in ergodic theory
mathematics, a measure-preserving dynamical system is an object of study in the abstract formulation of dynamical systems, and ergodic theory in particular
Measure-preserving dynamical system
Measure-preserving_dynamical_system
German pool player
earnings of $8,306. At this time Vogel also became a Cuetech and Dynamic Billiards sponsored player. Vogel's profile continued to rise following his
Felix_Vogel
Brazilian mathematician (born 1979)
all distinct. Other than that, Avila also did notable research on dynamical billiards. Later, as a research mathematician, he received in 2006 a CNRS Bronze
Artur_Avila
Indian theoretical physicist
Matrix theory to anyon gases, theorems and statistics for integrable billiards and nodal domains, quantum modes built on chaotic motion, Poincaré recurrence
Sudhir_Ranjan_Jain
Italian mathematician (born 1979)
scientific interests are in the field of dynamical systems, specifically, in the study of Hamiltonian dynamical systems by means of variational methods
Alfonso Sorrentino (mathematician)
Alfonso_Sorrentino_(mathematician)
German physicist (born 1952)
as the Big Bang; these investigation lead to models with chaotic dynamical billiards, in the case of classical general relativity theory in three dimensions
Hermann_Nicolai
Quadrilateral symmetric across a diagonal
have been studied in connection with outer billiards, a problem in the advanced mathematics of dynamical systems. A kite is a quadrilateral with reflection
Kite_(geometry)
applications in outer billiards, digital filters, and granular mixing. Goetz, Arek (2003). "Piecewise Isometries — an Emerging Area of Dynamical Systems". Fractals
Piecewise_isometry
Italian mathematician (born 1980)
dynamical systems. With Krzysztof Frączek in 2013, Ulcigrai is known for proving that in the Ehrenfest model (a mathematical abstraction of billiards
Corinna_Ulcigrai
Mathematical award
Prize in Dynamical Systems, abbreviated as the Brin Prize, is awarded to mathematicians who have made outstanding advances in the field of dynamical systems
Michael Brin Prize in Dynamical Systems
Michael_Brin_Prize_in_Dynamical_Systems
Russian billiards player and coach
in Kazan) is a Russian billiards player, the two-time European champion in Russian pyramid, the champion of Moscow in dynamic pyramid, and a Russian Master
Anastasia_Luppova
Metric space
research are developments of dynamical billiards in polyhedral spaces, e.g. of nonpositive curvature (hyperbolic billiards). Positively curved polyhedral
Polyhedral_space
situations. Anosov diffeomorphisms of the torus.[citation needed] Dynamical billiards, in which case the covering is countable.[citation needed] Markov
Markov_partition
Branch of mathematics that studies dynamical systems
averages of various functions along trajectories of dynamical systems. The notion of deterministic dynamical systems assumes that the equations determining
Ergodic_theory
American mathematician
she used to prove exponential correlation delay in Sinai billiards and other hyperbolic dynamical systems. Although born and raised in Hong Kong, Young came
Lai-Sang_Young
Rotation of a circle by an angle of π times an irrational number
Tabachnikov, Serge (2002). "Rational Billiards and Flat Structures". In Hasselblatt, B.; Katok, A. (eds.). Handbook of Dynamical Systems (PDF). Vol. IA. Elsevier
Irrational_rotation
theory, mathematical logic, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations. Some problems belong to more
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
polarisation Dynamic pressure Dynamic scattering mode Dynamic speckle Dynamic stall Dynamic structure factor Dynamical billiards Dynamical friction Dynamical horizon
Index_of_physics_articles_(D)
Spanish mathematician (born 1973)
Miranda Galcerán is a Spanish mathematician specializing in geometry and dynamical systems, especially in symplectic geometry. Miranda earned a bachelor's
Eva_Miranda
Randomness and Dynamical Systems" (1974) Yale University Press, ISBN 0-300-01745-6 Ya.G. Sinai, (1959) "On the Notion of Entropy of a Dynamical System", Doklady
Ornstein_isomorphism_theorem
This is a list of famous Taiwanese people. People who were not born in Taiwan are indicated by an asterisk (*, notation incomplete). Alien Huang Hong sheng
List_of_Taiwanese_people
In mathematics, an interval exchange transformation is a kind of dynamical system that generalises circle rotation. The phase space consists of the unit
Interval exchange transformation
Interval_exchange_transformation
Name used for Russian and Belarusian athletes at the 2025 World Games
Sport Men Women Total Billiards sports 0 1 1 Dancesport 1 1 2 Karate 1 0 1 Freediving 3 1 4 Finswimming 3 6 9 Muaythai 1 2 3 Sambo 5 5 10 Wakeboarding
Individual Neutral Athletes at the 2025 World Games
Individual_Neutral_Athletes_at_the_2025_World_Games
European Pool Championships, April/May 2019
The 2019 European Pool Championships (also known as the 2019 Dynamic Billiards European Pool Championships) was a series of professional pool championships
2019 European Pool Championship
2019_European_Pool_Championship
American mathematician
Applied Mathematics at Cornell University, where he worked on quantum billiards. He was supervised by Richard Liboff and graduated in 2002 with a PhD
Mason_Porter
Cue sport
Principles of Pool and Billiards (ebook). Union Square & Company. ISBN 9781454927914. Alciatore, David G. (May 2017). The Sport of Pool Billiards 1: Techniques
Straight_pool
American composer
at the Pennsylvania State University. Shor’s research focused on billiards, dynamical systems, Lie groups, and non-Euclidean geometry. In 1996, he obtained
Alexey_Shor
American mathematician
groups act. He has worked on what mathematicians refer to as billiards, which are dynamical systems based on a convex shape in a plane. He has explored
Richard Schwartz (mathematician)
Richard_Schwartz_(mathematician)
In physics, two bodies contacting each other
two balls is 90 degrees. This is an important fact that professional billiards players take into account, although it assumes the ball is moving without
Collision
Country in East Asia
doi:10.1080/14623528.2020.1848109. Harris, Luke J. (2020). "Snooker and Billiards". In Nauright, John; Zipp, Sarah (eds.). Routledge Handbook of Global
China
European governing body for pocket billiards
Billiard Federation (EPBF) is the European governing body for pocket billiards. EPBF is the European regional affiliate member of the World Pool-Billiard
European Pocket Billiard Federation
European_Pocket_Billiard_Federation
holomorphic 1-form. These surfaces arise in dynamical systems where they can be used to model billiards, and in Teichmüller theory. A particularly interesting
Translation_surface
Sporting event delegation
Men Women Total Air sports 1 2 3 Archery 4 4 8 Beach handball 10 10 20 Billiards 7 5 12 Boules sports 2 2 4 Canoe sports 14 14 28 Cheerleading 3 1 4 Dancesport
China_at_the_2025_World_Games
Multi-sport club in Cyprus
rival teams. AEL's HEADQUARTERS were located in the "DYNAMIC PoolHall". The first roster of AEL billiards club consisted of: The cycling team was founded in
AEL_Limassol
Russian mathematician and mathematical physicist
is a Russian mathematician and mathematical physicist, specializing in dynamical systems of classical mechanics. Treschev completed his secondary study
Dmitrii_Treschev
Russian mathematician and mathematical physicist
and Dynamical Astronomy, vol. 54, 1992, pp. 393–399 doi:10.1007/BF00049149 Kozlov, Valeriĭ V.; Treshchëv, Dmitriĭ V. (5 August 1991). Billiards: A Genetic
Valery_Vasilevich_Kozlov
Iranian mathematician (1977–2017)
at Stanford University. Her research focused on hyperbolic geometry, dynamical systems, complex analysis, and topology. In 2014, she was awarded the
Maryam_Mirzakhani
Concept in mathematics
curvature, cf Hadamard billiards. Structural stability of the system provides a justification for applying the qualitative theory of dynamical systems to analysis
Structural_stability
German pool player (born 1997)
the MVP award at the 2017, 2022 and 2023 events. Filler started to play billiards at the age of seven, competing at a national level by 2007 (age 10). In
Joshua_Filler
American mathematician
(born in 1956) is an American mathematician who works in geometry and dynamical systems. He is currently a Professor of Mathematics at Pennsylvania State
Sergei_Tabachnikov
Motion of particles in a fluid
isomorphism here is that of the isomorphism of dynamical systems. Many dynamical systems, including Sinai's billiards and Anosov flows are isomorphic to Bernoulli
Flow_(mathematics)
Topics referred to by the same term
mixed with stimulants Cue ball, the ball struck with the cue stick in billiards, pool, snooker, and other cue sports Cueball Carmichael, American professional
Q-ball_(disambiguation)
Jerald Ericksen (1924–2021) Alex Eskin (b. 1965), researcher in rational billiards and geometric group theory Christina Eubanks-Turner, American mathematics
List of American mathematicians
List_of_American_mathematicians
Sporting event delegation
Sport Men Women Total Air sports 1 0 1 Archery 2 1 2 Billiards 0 1 1 Boules sports 1 1 2 Canoe dragon boat 11 11 22 Canoe marathon 2 2 4 Canoe polo 8
Spain_at_the_2025_World_Games
Generalization of the Bernoulli process to more than two possible outcomes
symbolic dynamics, and are thus important in the study of dynamical systems. Many important dynamical systems (such as Axiom A systems) exhibit a repellor
Bernoulli_scheme
2020 nine-ball pool competition
2020 Dynamic Billard Treviso Open". AzBilliards. Archived from the original on 13 August 2021. Retrieved 13 August 2021. House, WUM Brand. "Dynamic Billard
2020_Treviso_Open
Chinese pool player (born 1993)
Kelly Fisher 9–3 in the final, and later won the All Japan Championship. Billiards Digest named Chen as 2011 player of the year after reaching the final
Chen_Siming
French mathematician
her work on Hamiltonian dynamical systems, and in particular on the regularity of invariant curves in the dynamics of billiards. She was named to the Institut
Marie-Claude_Arnaud
Country in Northwestern Europe
league, rugby sevens, golf, boxing, netball, water polo, field hockey, billiards, darts, rowing, rounders and cricket originated or were substantially
United_Kingdom
This is a list of notable people from Delhi, India. Ratish Nanda, conservation architect Anurag Anand Asloob Ahmad Ansari Chetan Bhagat Bedil Dehlavi (1642–1720)
List_of_people_from_Delhi
Part of the human body where the legs join the torso
(2000): 2486–2488. Byrne, Robert. Byrne's new standard book of pool and billiards. Houghton Mifflin Harcourt, 1998. Guthrie, R. Dale. 2006. The Nature of
Crotch
American mathematician (born 1953)
1953, in Ithaca, New York) is an American mathematician, specializing in dynamical systems. His father, David Smillie, was a professor of psychology. John
John_Smillie_(mathematician)
Straits Times, p. A10. "IBSF Long up Billiards Championships Long up – Leeds / England 2013". International Billiards and Snooker Federation. Archived from
List of Singapore world champions in sports
List_of_Singapore_world_champions_in_sports
Ability of a computing system to simulate Turing machines
DNA computers have been shown to be Turing-equivalent Physical systems: Billiards Many computational languages exist that are not Turing-complete. One such
Turing_completeness
Sporting event delegation
Athlete Event Qualification Final Balance Exercise Dynamic Exercise Total Score Rank Score Rank Score Rank Score Rank Andreas Benke Aaron Borck Pascale
Germany at the 2025 World Games
Germany_at_the_2025_World_Games
Sony Computer Entertainment Sony Computer Entertainment 2000-07-27JP Billiards Xciting •Simple 2000 Series Vol. 14: The BilliardJP Agenda D3 PublisherJP
List of PlayStation 2 games (A–K)
List_of_PlayStation_2_games_(A–K)
Dutch pool player (born 1977)
However, he lost to Efren Reyes. In 2004, he won the inaugural Skins Billiards Championship with prize money of US$42,500. Feijen has won the European
Niels_Feijen
table-top cue sports. These events include snooker, pool disciplines and billiards. Whilst these are traditionally singles sports, some matches and tournaments
2019_in_cue_sports
Results (2022) Results (2023) Results (2024) Results (2025) (Formation Skydiving) Results (2025) (Artistic Events and Dynamic) FAI Results Website v t e
World Indoor Skydiving Championships
World_Indoor_Skydiving_Championships
no Senjou" Ving Ving October 1, 1998 Unreleased Unreleased Backstreet Billiards Agenda ArgentJP, ASCII EntertainmentNA July 30, 1998 Unreleased October
List of PlayStation (console) games (A–L)
List_of_PlayStation_(console)_games_(A–L)
Use of the second law of thermodynamics to distinguish past from future
exactly-solvable continuous-time ergodic systems, such as Hadamard's billiards, or the Anosov flow on the tangent space of PSL(2,R). Another distinct
Entropy_as_an_arrow_of_time
investigate several haunted buildings; The Gatley Building, a former saloon and billiards hall from 1898 where a possible murder weapon could have bee thrown down
List of Ghost Adventures episodes
List_of_Ghost_Adventures_episodes
Association of Summer Olympic International Federations (ASOIF). includes Carom billiards, Pool & Snooker Provisional member, pending ratification by ARISF general
List of international sports federations
List_of_international_sports_federations
March 1882 Morgan Earp, Sheriff Pete Spence (accused) Shot while playing billiards at the Campbell & Hatch Billiard Parlor in Tombstone, Arizona by Cowboys
List_of_assassinations
Notable People from Bengaluru
Prakash Padukone – badminton player Ashwini Ponnappa Pankaj Advani – billiards and snooker World Champion Mayank Agarwal – Indian cricketer John Bean
List_of_people_from_Bengaluru
Platformer HAL Laboratory Nintendo March 15 Side Pocket NS Port Sports (billiards/pool) Data East March 15 Wolcen: Lords of Mayhem PS4, XBO Action RPG Wolcen
List of video games released in 2023
List_of_video_games_released_in_2023
Chinese-American mathematician
Professor of Mathematics. His research deals with celestial mechanics, dynamical systems, Hamiltonian dynamics, and ergodic theory. In his dissertation
Zhihong_Xia
boxing, rugby league, rugby union, cricket, field hockey, snooker, darts, billiards, squash, curling and badminton, all of which are popular in Britain. Another
Culture_of_the_United_Kingdom
Championship for National Teams". Retrieved September 22, 2024. "Artistic Billiards World Championship". Retrieved September 22, 2024. "WCBS Championship"
2024_in_precision_sports
maintain their frame rate target more consistently. Games utilizing a dynamic resolution will hit their max resolution more often, or at all times due
List of backward-compatible games for Xbox One and Series X/S
List_of_backward-compatible_games_for_Xbox_One_and_Series_X/S
athlete 1 August – Robby Langers, footballer 20 September – Fonsy Grethen, billiards player 26 November – Claude Turmes, politician 4 December – Eugène Berger
1960_in_Luxembourg
2020. "Black Belt (1986)". GameSpot. Retrieved July 7, 2020. "Champion Billiards". GameSpot. Archived from the original on March 27, 2019. Retrieved July
List_of_Sega_video_games
Third planet from the Sun
102896. ISSN 0012-8252. "Is a Pool Ball Smoother than the Earth?" (PDF). Billiards Digest. 1 June 2013. Archived (PDF) from the original on 4 September 2014
Earth
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DYNAMICAL BILLIARDS
DYNAMICAL BILLIARDS
DYNAMICAL BILLIARDS
DYNAMICAL BILLIARDS
DYNAMICAL BILLIARDS
DYNAMICAL BILLIARDS
DYNAMICAL BILLIARDS
DYNAMICAL BILLIARDS
DYNAMICAL BILLIARDS
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