Recurrence, dimensions and Lyapunov exponents
B. Saussol, S. Troubetzkoy, S. Vaienti
TL;DR
This paper investigates the relationship between recurrence times, dimensions, and Lyapunov exponents in dynamical systems, providing new formulas and bounds for these quantities in specific cases.
Contribution
It introduces novel connections between return times, Lyapunov exponents, and dimensions for one-dimensional maps, expanding understanding of dynamical invariants.
Findings
Poincaré return time of a typical cylinder is at least its length
Lyapunov exponent and dimension can be expressed via return times for one-dimensional maps
Established bounds and relationships between recurrence times and dynamical invariants
Abstract
We show that the Poincar\'e return time of a typical cylinder is at least its length. For one dimensional maps we express the Lyapunov exponent and dimension via return times.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Differential Equations and Dynamical Systems · Quantum chaos and dynamical systems