SRB measures for higher dimensional singular partially hyperbolic attractors. (Mesures SRB pour des attracteurs partiellement hyperboliques avec singularité(s) en dimension finie quelconque.) (English. French summary) Zbl 1403.37041
Summary: We prove the existence and the uniqueness of the SRB measure for any singular hyperbolic attractor in dimension \(d \geq 3\). The proof does not use Poincaré sectional maps, but uses basic properties of thermodynamical formalism.
MSC:
| 37D35 | Thermodynamic formalism, variational principles, equilibrium states for dynamical systems |
| 37A35 | Entropy and other invariants, isomorphism, classification in ergodic theory |
| 37A60 | Dynamical aspects of statistical mechanics |
| 37D20 | Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) |
| 47N10 | Applications of operator theory in optimization, convex analysis, mathematical programming, economics |
Keywords:
partially hyperbolic singular flows; thermodynamical formalism; equilibrium states; SRB and physical measuresReferences:
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