Sharp polynomial bounds on decay of correlations for multidimensional nonuniformly hyperbolic systems and billiards. (Bornes polynomiales précises pour la décroissance des corrélations d’applications non-uniformément hyperboliques en plusieurs dimensions et de billards.) (English. French summary) Zbl 1498.37053
The paper concerns optimal and lower bounds for subexponential decay of correlations. The results apply to planar dispersing billiards and piecewise smooth nonuniformly expanding nonmarkovian maps with neutral fixed point. To this end, the authors extends the operator renewal theory of S. Gouëzel [Isr. J. Math. 139, 29–65 (2004, Zbl 1070.37003)] and O. M. Sarig [Invent. Math. 150, 629–653 (2002; Zbl 1042.37005)].
Reviewer: Martin Sambarino (Montevideo)
MSC:
| 37D25 | Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) |
| 37C30 | Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. |
| 37A25 | Ergodicity, mixing, rates of mixing |
| 47A35 | Ergodic theory of linear operators |
| 60K05 | Renewal theory |
| 37H12 | Random iteration |
Keywords:
sharp mixing rates; nonuniform hyperbolicity; billiards; multidimensional intermittent maps; operator renewal theoryReferences:
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