Stably ergodic diffeomorphisms which are not partially hyperbolic

Abstract

We show stable ergodicity of a class of conservative diffeomorphisms of T n which do not have any hyperbolic invariant subbundle. Moreover, the uniqueness of SRB (Sinai-Ruelle-Bowen) measure for non-conservative C 1 perturbations of such diffeomorphisms is verified. This class strictly contains non-partially hyperbolic robustly transitive diffeomorphisms constructed by Bonatti-Viana [BV00] and so we answer the question posed there on the stable ergodicity of such systems.

On the regularization of conservative maps

“…(3) The existence of locally generic non-uniformly hyperbolic ergodic conservative diffeomorphisms with non-simple Lyapunov spectrum [9], [25] (the proof, conditional to the existence of regularization, is nicely sketched in [7, p. 260]).…”

Evaluation of the effect of nutrient ratios on biosurfactant production by Serratia marcescens using a Box-Behnken design

“…The culture conditions used for biosurfactant production by means of Serratia marcescens have been studied in terms of the carbon source, pH and temperature [14]. Nevertheless, several authors point out that the concentrations of Fe and Mg affect biosurfactant production in other microorganisms [15,16]; moreover, the interactions among the C/N, C/Mg and C/ Fe ratios have not been examined for S. marcescens.…”

Robust ergodic properties in partially hyperbolic dynamics

“…According to Pliss' Lemma, there are some l ≥ kδ, where δ = λ+4 −h , and 0 The proof of Lemma 4.4 is inspired by [BDP02,Tah04]. Its strategy is to find…”