1,216 research outputs found
Entropy, Thermostats and Chaotic Hypothesis
The chaotic hypothesis is proposed as a basis for a general theory of
nonequilibrium stationary states.
Version 2: new comments added after presenting this talk at the Meeting
mentioned in the Acknowledgement. One typo corrected.Comment: 6 page
Singularities and nonhyperbolic manifolds do not coincide
We consider the billiard flow of elastically colliding hard balls on the flat
-torus (), and prove that no singularity manifold can even
locally coincide with a manifold describing future non-hyperbolicity of the
trajectories. As a corollary, we obtain the ergodicity (actually the Bernoulli
mixing property) of all such systems, i.e. the verification of the
Boltzmann-Sinai Ergodic Hypothesis.Comment: Final version, to appear in Nonlinearit
Separating Solution of a Quadratic Recurrent Equation
In this paper we consider the recurrent equation
for with and given. We give conditions
on that guarantee the existence of such that the sequence
with tends to a finite positive limit as .Comment: 13 pages, 6 figures, submitted to J. Stat. Phy
Ergodic Properties of Square-Free Numbers
We construct a natural invariant measure concentrated on the set of
square-free numbers, and invariant under the shift. We prove that the
corresponding dynamical system is isomorphic to a translation on a compact,
Abelian group. This implies that this system is not weakly mixing and has zero
measure-theoretical entropy.Comment: 37 page, 1 figur
Separating Solution of a Quadratic Recurrent Equation
In this paper we consider the recurrent equation
for with and given. We give conditions
on that guarantee the existence of such that the sequence
with tends to a finite positive limit as .Comment: 13 pages, 6 figures, submitted to J. Stat. Phy
An Elementary Proof of the Existence and Uniqueness Theorem for the Navier-Stokes Equations
We give a geometric approach to proving know regularity and existence
theorems for the 2D Navier-Stokes Equations. We feel this point of view is
instructive in better understanding the dynamics. The technique is inspired by
constructions in the Dynamical Systems.Comment: 15 Page
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