This clear book presents a critical and modern analysis of the conceptual foundations of
statistical mechanics as laid down in Boltzmann's works. The author emphasises the relation …

We establish general criteria for ergodicity and Bernoulliness for volume preserving
diffeormorphisms and flows on compact manifolds. We prove that every ergodic component …

For billiards with a hyperbolic behavior, Fundamental Theorems ensure an abundance of
geometrically nicely situated and sufficiently large stable and unstable invariant manifolds. A …

The mixing behavior of a hard-sphere gas has its origin in the exponential growth of small
perturbations in phase space. This instability is characterized by the so-called Lyapunov …

Proof of the Boltzmann-Sinai ergodic hypothesis for typical hard disk systems Page 1 DOI:
10.1007/s00222-003-0304-9 Invent. math. 154, 123–178 (2003) Proof of the Boltzmann-Sinai …

We consider the motion of n balls in billiard tables of a special form and we prove that the
resulting dynamical systems are ergodic on a constant energy surface; in fact, they enjoy the …

We consider the system of N (≧ 2) hard balls with masses m_ 1, ..., m_ N and radius r in the
flat torus T _ L^ ν= R^ ν/L ⋅ Z^ ν of size L, ν ≧ 3. We prove the ergodicity (actually, the …

We consider the system of N (≥ 2) elastically colliding hard balls with masses m1,..., mN,
radius r, moving uniformly in the flat torus TL ν= Rν/L· Zν, ν≥ 2. It is proved here that the …

An overview of the history of Ludwig Boltzmann's more than one hundred year old ergodic
hypothesis is given. The existing main results, the majority of which is connected with the …

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 …