Ruelle inequality of folding type for \(C^{1+\alpha}\) maps. (English) Zbl 1421.37012
Summary: For all \(C^{1+\alpha}\) maps, we prove an inequality conjectured by Ruelle that the metric entropy is bounded from above by the folding entropy minus the sum of the negative Lyapunov exponents.
MSC:
| 37C40 | Smooth ergodic theory, invariant measures for smooth dynamical systems |
| 37A35 | Entropy and other invariants, isomorphism, classification in ergodic theory |
| 37D25 | Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) |
| 37D35 | Thermodynamic formalism, variational principles, equilibrium states for dynamical systems |
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