Lyapunov optimization for non-generic one-dimensional expanding Markov maps

Lyapunov Exponents and Rates of Mixing for One-dimensional Maps

We show that one dimensional maps f with strictly positive Lyapunov exponents almost everywhere admit an absolutely continuous invariant measure. If f is topologically transitive some power of f is mixing and in particular the correlation of Hölder continuous observables decays to zero. The main objective of this paper is to show that the rate of decay of correlations is determined, in some sit...

Lyapunov optimizing measures for C1 expanding maps of the circle

For a generic C expanding map of the circle, the Lyapunov maximizing measure is unique, fully supported, and has zero entropy.

Induced Maps , Markov Extensions and Invariantmeasures in One - Dimensional Dynamics

- Generic Cocycles Have One - Point Lyapunov Spectrum

We show the sum of the first k Lyapunov exponents of linear cocycles is an upper semicontinuous function in the L topologies, for any 1 ≤ p ≤ ∞ and k. This fact, together with a result from Arnold and Cong, implies that the Lyapunov exponents of the L-generic cocycle, p < ∞, are all equal.

One-dimensional Optimization on Non-archimedean Fields

One dimensional optimization on non-Archimedean fields is presented. We derive first and second order necessary and sufficient optimality conditions. For first order optimization, these conditions are similar to the corresponding real ones; but this is not the case for higher order optimization. This is due to the total disconnectedness of the given non-Archimedean field in the order topology, ...