About: Hadamard's dynamical system

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In physics and mathematics, the Hadamard dynamical system (also called Hadamard's billiard or the Hadamard–Gutzwiller model) is a chaotic dynamical system, a type of dynamical billiards. Introduced by Jacques Hadamard in 1898, and studied by Martin Gutzwiller in the 1980s, it is the first dynamical system to be proven chaotic.

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rdfs:label	Hadamard's dynamical system (en)
rdfs:comment	In physics and mathematics, the Hadamard dynamical system (also called Hadamard's billiard or the Hadamard–Gutzwiller model) is a chaotic dynamical system, a type of dynamical billiards. Introduced by Jacques Hadamard in 1898, and studied by Martin Gutzwiller in the 1980s, it is the first dynamical system to be proven chaotic. (en)
dct:subject	Chaotic maps Ergodic theory
Wikipage page ID	5424787 (xsd:integer)
Wikipage revision ID	993727564 (xsd:integer)
Link from a Wikipage to another Wikipage	Riemann surface Dynamical billiards Dynamical system Mathematics Geodesic Chaotic maps Subatomic particle Friction Hamiltonian (quantum mechanics) Hamilton–Jacobi equation Physics Albert Einstein Curvature Ernst Mach Jacques Hadamard Ergodic theory Chaos theory Martin Gutzwiller Bolza surface Metric tensor Yakov Sinai Lyapunov exponent Conjugate momenta Sinai's billiards
sameAs	Hadamard's dynamical system Hadamard's dynamical system Hadamard's dynamical system Hadamard's dynamical system
dbp:wikiPageUsesTemplate	dbt:Reflist dbt:Short_description
has abstract	In physics and mathematics, the Hadamard dynamical system (also called Hadamard's billiard or the Hadamard–Gutzwiller model) is a chaotic dynamical system, a type of dynamical billiards. Introduced by Jacques Hadamard in 1898, and studied by Martin Gutzwiller in the 1980s, it is the first dynamical system to be proven chaotic. The system considers the motion of a free (frictionless) particle on the Bolza surface, i.e, a two-dimensional surface of genus two (a donut with two holes) and constant negative curvature; this is a compact Riemann surface. 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. (en)
gold:hypernym	System
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page length (characters) of wiki page	4043 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Hadamard's_dynamical_system
is Link from a Wikipage to another Wikipage of	Hadamard (disambiguation) List of things named after Jacques Hadamard Hadamard's billiard Hadamard's billiards Hadamard-Gutzwiller model Hadamard billiards Hadamard dynamical system Hadamard–Gutzwiller model
is Wikipage redirect of	Hadamard's billiard Hadamard's billiards Hadamard-Gutzwiller model Hadamard billiards Hadamard dynamical system Hadamard–Gutzwiller model
is Wikipage disambiguates of	Hadamard (disambiguation)
is foaf:primaryTopic of	wikipedia-en:Hadamard's_dynamical_system

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