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- Hadamard's_dynamical_system abstract "In physics and mathematics, the Hadamard dynamical system or Hadamard's billiard is a chaotic dynamical system, a type of dynamical billiards. Introduced by Jacques Hadamard in 1898, it is the first dynamical system to be proven chaotic.The system considers the motion of a free (frictionless) particle on a surface of constant negative curvature, the simplest compact Riemann surface, which is the surface of genus two: a donut with two holes. Hadamard was able to show that every particle trajectory moves away from every other: that all trajectories have a positive Lyapunov exponent.Frank Steiner argues that Hadamard's study should be considered to be the first-ever examination of a chaotic dynamical system, and that Hadamard should be considered the first discoverer of chaos. He points out that the study was widely disseminated, and considers the impact of the ideas on the thinking of Albert Einstein and Ernst Mach.The system is particularly important in that in 1963, Yakov Sinai, in studying Sinai's billiards as a model of the classical ensemble of a Boltzmann–Gibbs gas, was able to show that the motion of the atoms in the gas follow the trajectories in the Hadamard dynamical system.".
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- Hadamard's_dynamical_system wikiPageRevisionID "598830633".
- Hadamard's_dynamical_system hasPhotoCollection Hadamard's_dynamical_system.
- Hadamard's_dynamical_system subject Category:Chaotic_maps.
- Hadamard's_dynamical_system subject Category:Ergodic_theory.
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- Hadamard's_dynamical_system type Representation104076846.
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- Hadamard's_dynamical_system comment "In physics and mathematics, the Hadamard dynamical system or Hadamard's billiard is a chaotic dynamical system, a type of dynamical billiards. Introduced by Jacques Hadamard in 1898, it is the first dynamical system to be proven chaotic.The system considers the motion of a free (frictionless) particle on a surface of constant negative curvature, the simplest compact Riemann surface, which is the surface of genus two: a donut with two holes.".
- Hadamard's_dynamical_system label "Hadamard's dynamical system".
- Hadamard's_dynamical_system sameAs m.0dl97_.
- Hadamard's_dynamical_system sameAs Q5637574.
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- Hadamard's_dynamical_system sameAs Hadamard's_dynamical_system.
- Hadamard's_dynamical_system wasDerivedFrom Hadamard's_dynamical_system?oldid=598830633.
- Hadamard's_dynamical_system isPrimaryTopicOf Hadamard's_dynamical_system.