A conjecture is formulated and discussed which provides necessary and su cient condition for the ... more A conjecture is formulated and discussed which provides necessary and su cient condition for the ergodicity of cylindric billiards (this conjecture improves a previous one of the second author). This condition requires that the action of a Lie-subgroup G of the orthogonal group O(d) (d being the dimension of the billiard in question) be transitive on the unit sphere S d?1. If C 1
A further step is achieved toward establishing the celebrated Boltzmann-Sinai ergodic hypothesis:... more A further step is achieved toward establishing the celebrated Boltzmann-Sinai ergodic hypothesis: for systems of four hard balls on the ν-torus (ν>2) it is shown that, on the submanifold of the phase specified by the trivial conservation laws, the system is aK-flow. All parts of our previous demonstration providing the analogous result for three hard balls are simplified and strengthened.
We consider the system of N (≥ 2) elastically colliding hard balls with masses m 1 ,. .. , m N , ... more We consider the system of N (≥ 2) elastically colliding hard balls with masses m 1 ,. .. , m N , radius r, moving uniformly in the flat torus T ν L = R ν /L • Z ν , ν ≥ 2. It is proved here that the relevant Lyapunov exponents of the flow do not vanish for almost every (N + 1)-tuple (m 1 ,. .. , m N ; L) of the outer geometric parameters.
We survey applications of the theory of hyperbolic (and to a lesser extent non hyperbolic) billia... more We survey applications of the theory of hyperbolic (and to a lesser extent non hyperbolic) billiards to some fundamental problems of statistical physics and their mathematically rigorous derivations in the framework of classical Hamiltonian systems.
We consider a one-dimensional system consisting of a tagged particle of massM surrounded by a gas... more We consider a one-dimensional system consisting of a tagged particle of massM surrounded by a gas of unit-mass hard-point particles in thermal equilibrium. Denoting byQ t the displacement of the tagged particle, we give lower and upper boundsindependent ofM ...
A conjecture is formulated and discussed which provides necessary and su cient condition for the ... more A conjecture is formulated and discussed which provides necessary and su cient condition for the ergodicity of cylindric billiards (this conjecture improves a previous one of the second author). This condition requires that the action of a Lie-subgroup G of the orthogonal group O(d) (d being the dimension of the billiard in question) be transitive on the unit sphere S d?1. If C 1
A further step is achieved toward establishing the celebrated Boltzmann-Sinai ergodic hypothesis:... more A further step is achieved toward establishing the celebrated Boltzmann-Sinai ergodic hypothesis: for systems of four hard balls on the ν-torus (ν>2) it is shown that, on the submanifold of the phase specified by the trivial conservation laws, the system is aK-flow. All parts of our previous demonstration providing the analogous result for three hard balls are simplified and strengthened.
We consider the system of N (≥ 2) elastically colliding hard balls with masses m 1 ,. .. , m N , ... more We consider the system of N (≥ 2) elastically colliding hard balls with masses m 1 ,. .. , m N , radius r, moving uniformly in the flat torus T ν L = R ν /L • Z ν , ν ≥ 2. It is proved here that the relevant Lyapunov exponents of the flow do not vanish for almost every (N + 1)-tuple (m 1 ,. .. , m N ; L) of the outer geometric parameters.
We survey applications of the theory of hyperbolic (and to a lesser extent non hyperbolic) billia... more We survey applications of the theory of hyperbolic (and to a lesser extent non hyperbolic) billiards to some fundamental problems of statistical physics and their mathematically rigorous derivations in the framework of classical Hamiltonian systems.
We consider a one-dimensional system consisting of a tagged particle of massM surrounded by a gas... more We consider a one-dimensional system consisting of a tagged particle of massM surrounded by a gas of unit-mass hard-point particles in thermal equilibrium. Denoting byQ t the displacement of the tagged particle, we give lower and upper boundsindependent ofM ...
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Papers by Domokos Szász