2012/09/30 by Eleonora Catsigeras, ELEONORA CATSIGERAS, Marcelo Cerminara +3 · 37 citations
Mathematics · Physics and Astronomy · #Boltzmann's entropy formula #Bounded function #Chaos control and synchronization #Entropy (arrow of time) #Ergodic theory #Invariant (physics) #Lyapunov exponent #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Topological entropy #math.DS
paper · pdf · doi:10.1017/etds.2013.93
published in Ergodic Theory and Dynamical Systems 35(3), 737-761 (Cambridge University Press) · We added the corrections suggested by the referee. Accepted for publication in the journal "Ergodic Theory and Dynamical Systems". Final version will appear in http://journals.cambridge.org/action/displayJournal?jid=ets
arxiv created 2013/09/11 · openalex publication_date 2014/02/26 · openalex created_date 2016/06/24 · arxiv updated 2016/06/28 · openalex updated_date 2026/08/05
Abstract For any C1 diffeomorphism with dominated splitting, we consider a non-empty set of invariant measures that describes the asymptotic statistics of Lebesgue-almost all orbits. They are the limits of convergent subsequences of averages of the Dirac delta measures supported on those orbits. We prove that the metric entropy of each of these measures is bounded from below by the sum of the Lyapunov exponents on the dominating sub-bundle. As a consequence, if those exponents are non-negative, and if the exponents on the dominated sub-bundle are non-positive, those measures satisfy the Pesin entropy formula.