Open AccessSRB measures and Pesin’s entropy formula for endomorphisms
Author(s) -
Min Qian,
Shu Zhu
Publication year - 2001
Publication title -
transactions of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.798
H-Index - 100
eISSN - 1088-6850
pISSN - 0002-9947
DOI - 10.1090/s0002-9947-01-02792-1
Subject(s) - endomorphism , mathematics , invertible matrix , entropy (arrow of time) , pure mathematics , thermodynamics , physics
We present a formulation of the SRB (Sinai-Ruelle-Bowen) property for invariant measures of C 2 C^2 endomorphisms (maybe non-invertible and with singularities) of a compact manifold via their inverse limit spaces, and prove that this property is necessary and sufficient for Pesin’s entropy formula. This result is a non-invertible endomorphisms version of a result of Ledrappier, Strelcyn and Young.