caa a22 4500 467892415 CHVBK 20180406152752.0 cr unu---uuuuu 170328e20060301xx s 000 0 eng 10.1007/s10955-005-8024-8 doi (NATIONALLICENCE)springer-10.1007/s10955-005-8024-8 Wolf Christian Department of Mathematics, Wichita State University, 67260, Wichita, KS, USA aut Generalized Physical and SRB Measures for Hyperbolic Diffeomorphisms [Elektronische Daten] [Christian Wolf] In this paper we introduce the notion of generalized physical and SRB measures. These measures naturally generalize classical physical and SRB measures to measures which are supported on invariant sets that are not necessarily attractors. We then perform a detailed case study of these measures for hyperbolic Hènon maps. For this class of systems we are able to develop a complete theory about the existence, uniqueness, finiteness, and properties of these natural measures. Moreover, we derive a classification for the existence of a measure of full dimension. We also consider general hyperbolic surface diffeomorphisms and discuss possible extensions of, as well as the differences to, the results for Hènon maps. Finally, we study the regular dependence of the dimension of the generalized physical/SRB measure on the diffeomorphism. For the proofs we apply various techniques from smooth ergodic theory including the thermodynamic formalism. Springer Science + Business Media, Inc., 2006 Natural measures nationallicence SRB property nationallicence Physical measure nationallicence Axiom A nationallicence Hénon map nationallicence Hausdorff dimension nationallicence Journal of Statistical Physics Springer US; http://www.springer-ny.com 122/6(2006-03-01), 1111-1138 0022-4715 122:6<1111 2006 122 10955 https://doi.org/10.1007/s10955-005-8024-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-005-8024-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Wolf Christian Department of Mathematics, Wichita State University, 67260, Wichita, KS, USA aut NATIONALLICENCE 773 0- Journal of Statistical Physics Springer US; http://www.springer-ny.com 122/6(2006-03-01), 1111-1138 0022-4715 122:6<1111 2006 122 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer