RECURRENCE RATE IN RAPIDLY MIXING DYNAMICAL SYSTEMS

By B. Saussol. 2004

53 citations recorded by the source corpus.

For measure preserving dynamical systems on metric spaces we study the time needed by a typical orbit to return back close to its starting point. We prove that when the decay of correlation is super-polynomial the recurrence rates and the pointwise dimensions are equal. This gives a broad class of systems for which the recurrence rate equals the Hausdorff dimension of the invariant measure.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/01011c0d983c8df33884a55dff8a1d1f97907566

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Maria José Pacifico
2. Stefano Galatolo
3. N. Haydn
4. B. Saussol

In Mathematical Physics

1. N. Haydn
2. Stefano Galatolo
3. Maria José Pacifico
4. B. Saussol
5. Daniel Thompson

In Statistical and Nonlinear Physics

1. N. Haydn
2. Stefano Galatolo
3. Maria José Pacifico
4. B. Saussol
5. Daniel Thompson

Citations in the corpus

• Entry and return times distribution (2013, background): “This extends a previous result of Hirata, Saussol and Vaienti [7] where error estimates for P(ζ tU ) − e−t t r r! are given under the assumption that the partition {U, Uc} is φ-mixing or α-mixing (different error terms).”
• Lorenz-like flows: exponential decay of correlations for the Poincaré map, logarithm law, quantitative recurrence (2009, methodology): “Quantitative recurrence for Lorenz-like systems We now recall a general result proved by Saussol in [34] about quantitative recurrence in order to apply it to a Lorenz-like flow.”
• AN INTRODUCTION TO QUANTITATIVE POINCARÉ RECURRENCE IN DYNAMICAL SYSTEMS (2009, methodology): “In this section we prove Theorem 28 using the method developped in [52].”