2015/10/31 by Gerhard Keller · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Attractor #Chaos control and synchronization #Chaotic #Exponent #Formalism (music) #Interval (graph theory) #Markov chain #Markov process #Nonlinear Dynamics and Pattern Formation #Piecewise #Quantum chaos and dynamical systems #Skew #math.DS #msc:37AXX #msc:37D35
paper · pdf · doi:10.3934/dcdss.2017015
published as Discrete and Continuous Dynamical Systems - Series S 10 (2017), 313-334 · A minor mistake in Theorem 2 is corrected in the 2nd version
openalex created_date 2016/06/24 · openalex publication_date 2017/01/01 · arxiv created 2017/01/13 · arxiv updated 2018/03/01 · openalex updated_date 2026/08/05
Skew product systems with monotone one-dimensional fibre maps driven by piecewise expanding Markov interval maps may show the phenomenon of intermingled basins [1, 5, 16, 30]. To quantify the degree of intermingledness the uncertainty exponent [23] and the stability index [29, 20] were suggested and characterized (partially). Here we present an approach to evaluate/estimate these two quantities rigorously using thermodynamic formalism for the driving Markov map.