caa a22 4500 445391650 CHVBK 20180317143048.0 cr unu---uuuuu 170323e20110101xx s 000 0 eng 10.1007/s10955-010-0097-3 doi (NATIONALLICENCE)springer-10.1007/s10955-010-0097-3 Mihailescu Eugen Institute of Mathematics "Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, 014700, Bucharest, Romania aut Local Geometry and Dynamical Behavior on Folded Basic Sets [Elektronische Daten] [Eugen Mihailescu] We study new phenomena associated with the dynamics of higher dimensional non-invertible, hyperbolic maps f on basic sets of saddle type; the dynamics in this case presents important differences from the case of diffeomorphisms or expanding maps. We show that the stable dimension (i.e. the Hausdorff dimension of the intersection between local stable manifolds and the basic set) and the unstable dimension (similar definition) give a lot of information about the dynamical/ergodic properties of endomorphisms on folded basic sets. We prove a geometric flattening phenomenon associated to the stable dimension, i.e. we show that if the stable dimension is zero at a point, then the fractal Λ must be contained in a submanifold and f is expanding on Λ. We characterize folded attractors and folded repellers, as those basic sets with full unstable dimension, respectively with full stable dimension. We classify possible dynamical behaviors, and establish when is the system (Λ,f,μ) 1-sided or 2-sided Bernoulli for certain equilibrium measures μ on folded basic sets, for a class of perturbation maps. Springer Science+Business Media, LLC, 2010 Endomorphisms on folded basic sets of saddle type nationallicence Stable/unstable dimensions nationallicence 1-sided and 2-sided Bernoulli systems nationallicence Invariant manifolds nationallicence Hyperbolic attractors/repellers nationallicence Journal of Statistical Physics Springer US; http://www.springer-ny.com 142/1(2011-01-01), 154-167 0022-4715 142:1<154 2011 142 10955 https://doi.org/10.1007/s10955-010-0097-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-010-0097-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Mihailescu Eugen Institute of Mathematics "Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, 014700, Bucharest, Romania aut NATIONALLICENCE 773 0- Journal of Statistical Physics Springer US; http://www.springer-ny.com 142/1(2011-01-01), 154-167 0022-4715 142:1<154 2011 142 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer