Talk
Entropy for C1 diffeomorphisms
Talk by Prof. Dr. Todd Fisher
Date: 16.05.18 Time: 15.45 - 18.00 Room: ETH HG G 43
We will begin with classical properties of entropy for dynamical systems, and review a construction due to Newhouse that shows on surfaces one creates horseshoes from hyperbolic periodic orbits with large period through local perturbations. Adapting these techniques to higher dimensions our main theorem shows that, when one works in the C1 topology, the entropy of such horseshoes can be made arbitrarily close to an upper bound derived from Ruelle's inequality, i.e., the sum of the positive Lyapunov exponents (or the same for the inverse diffeomorphism, whichever is smaller). This optimal entropy creation yields a number of consequences for C1-generic diffeomorphisms. For instance, in the conservative settings, we find formulas for the topological entropy, deduce that the topological entropy is continuous but not locally constant at the generic diffeomorphism, and we prove that these generic diffeomorphisms have no measure of maximum entropy.