Entropy formula for endomorphisms: Relations between entropy, exponents and dimension
Min Qian Jian-Sheng Xie
Discrete & Continuous Dynamical Systems - A 2008, 21(2): 367-392 doi: 10.3934/dcds.2008.21.367
We present an entropy formula of Ledrappier-Young type for invariant measures (maybe non-SRB) of $ C^2 $ endomorphisms (maybe non-invertible and with singularities) on a compact manifold via their inverse limit spaces. This result may be considered as the most general form of entropy formula for a deterministic system with an invariant measure, and a preliminary step to Eckmann-Ruelle conjecture. As an important application, we have proved the exact dimensionality of ergodic measures invariant under expanding maps.
keywords: Lyapunov Exponents Entropy SRB Measure.

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