On the Statistical Distribution of First-Return Times of Balls and Cylinders in Chaotic Systems
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Summary
Bernoulli shifts, expanding maps of the interval and linear automorphisms of the two dimensional torus are considered, and relations linking these statistics with Renyi entropies and Lyapunov exponents are derived.
- Type
- article
- Published
- 2009-07-27
- Cited by
- 1
- References
- 34
- Access
- Open access
- OpenAlex
- https://openalex.org/W1976865261
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:17877156
Keywords
Phase space, Interval (graph theory), Chaotic, Bernoulli's principle, Moment (physics)
References
- Dimension theory in dynamical systems
- DNA, words and models
- Recurrence, Dimensions, and Lyapunov Exponents
- Thermodynamics of chaotic systems : an introduction
- Dimensions and entropies of strange attractors from a fluctuating dynamics approach
- Generalized dimensions, entropies, and Liapunov exponents from the pressure function for strange sets
- Hitting, returning and the short correlation function
- Generalized entropy decay rates of one-dimensional maps.
- Intermittency in chaotic systems and Renyi entropies
- Ergodic theory of chaos and strange attractors
- GENERALIZED ENTROPIES : RENYI AND CORRELATION INTEGRAL APPROACH
- Pointwise dimensions for Poincaré recurrences associated with maps and special flows
- Pesin's dimension for Poincare recurrences.
- Repetition times for Gibbsian sources
- Sharp error terms and neccessary conditions for exponential hitting times in mixing processes
- Dimensions for recurrence times: topological and dynamical properties
- LARGE DEVIATIONS FOR SHORT RECURRENCE
- The limiting distribution and error terms for return times of dynamical systems
- Estimation of the Kolmogorov entropy from a chaotic signal
- Multifractal Analysis of Local Entropies for Expansive Homeomorphisms with Specification
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