Return time statistics via inducing

By Henk Bruin, B. Saussol, Serge Troubetzkoy, Sandro Vaienti. Ergodic Theory and Dynamical Systems, 2000

65 citations recorded by the source corpus.

We prove that the return time statistics of a dynamical system do not change if one passes to an induced (i.e. first return) map. We apply this to show exponential return time statistics in (i) smooth interval maps with nowhere-dense critical orbits and (ii) certain interval maps with neutral fixed points. The method also applies to (iii) certain quadratic maps of the complex plane.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7df4d06df412d9d48b343f5299ec17eb7f3bbffa

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In Mathematical Physics

1. N. Haydn
2. J. Freitas
3. Mike Todd
4. A. C. Freitas

In Statistical and Nonlinear Physics

1. Mike Todd
2. N. Haydn

Citations in the corpus

• Hitting time statistics and extreme value theory (2008, background): “In [BT], the theory in [ BSTV ] was extended to show that for multimodal maps of the interval the RTS of suitable inducing schemes converge to the RTS of the original system.”
• Entry and return times distribution (2013, methodology): “For more specific systems, a number of results were shown in [15] (see also [31]) for the first return times.”