Physical measures for partially hyperbolic surface endomorphisms

Physical Measures for Partially Hyperbolic Surface Endomorphisms

We consider dynamical systems generated by partially hyperbolic surface endomorphisms of class Cr with one-dimensional strongly unstable subbundle. As the main result, we prove that such a dynamical system generically admits finitely many ergodic physical measures whose union of basins of attraction has total Lebesgue measure, provided that r ≥ 19.

Pointwise Dimension for Regular Hyperbolic Measures for Endomorphisms

Hyperbolic Saddle Measures and Laminarity for Holomorphic Endomorphisms of P2c

We study the laminarity of the Green current of endomorphisms of P2(C) near hyperbolic measures of saddle type. When these measures are supported by attracting sets, we prove that the Green current is laminar in the basin of attraction and we obtain new ergodic properties. This generalizes some results of Bedford and Jonsson on regular polynomial mappings in C2.

Hyperbolic Dynamics of Endomorphisms

We present the theory of hyperbolic dynamics of endomorphisms in. Topics covered are hyperbolic sets, stable manifolds, local product structure , shadowing, spectral decomposition and ^-stability. 0. Introduction In this paper we study a smooth mapping f of a manifold M as a dynamical system. We will discuss both semilocal and global dynamical properties of f, but always under some hyperbolicit...

Endomorphisms of Relatively Hyperbolic Groups

We generalize some results of Paulin and Rips-Sela on endomorphisms of hyperbolic groups to relatively hyperbolic groups, and in particular prove the following. • If G is a non-elementary relatively hyperbolic group with slender parabolic subgroups, and either G is not co-Hopfian or Out(G) is infinite, then G splits over a slender group. • If H is a non-parabolic subgroup of a relatively hyperb...