Eleonora Catsigeras

The Pesin entropy formula for diffeomorphisms with dominated splitting

For any

Equilibrium states and SRB-like measures of

C^1

C^1

n 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.

-expanding maps of the circle

For any C 1 expanding map f of the circle we study the equilibrium states for the potential = logjf 0 j. We formulate a C 1 generalization of Pesin’s Entropy Formula that holds for all the SRB measures if they exist, and for all the (necessarily existing) SRB-like measures. In theC 1 -generic case Pesin’s Entropy Formula holds for a unique SRB measure which is not absolutely continuous with respect to Lebesgue. The result also stands in the non generic case for which no SRB measure exists.

Observable Optimal State Points of Subadditive Potentials

For a sequence of subadditive potentials, n a method of choosing n state points with negative growth rates for an ergodic ndynamical system was given in [5]. This paper first ngeneralizes this result to the non-ergodic dynamics, and then nproves that under some mild additional hypothesis, one can choose npoints with negative growth rates from a positive Lebesgue measure nset, even if the system does not preserve any measure that is nabsolutely continuous with respect to Lebesgue measure.

Dominated splitting, partial hyperbolicity and positive entropy

Let

Oscillating Statistics of Transitive Dynamics

f:Mrightarrow M

Dynamics of large cooperative pulsed-coupled networks

be a

Dale's Principle Is Necessary for an Optimal Neuronal Network's Dynamics

C^1

Simultaneous continuation of infinitely many sinks at homoclinic bifurcations

diffeomorphism with a dominated splitting on a compact Riemanian manifold