Global-local mixing for infinite measure dynamical systems
Douglas Coates, Ian Melbourne
TL;DR
This paper establishes global-local mixing properties for a broad class of infinite measure dynamical systems, including various intermittent maps and complex parabolic rational maps, expanding understanding of their long-term statistical behavior.
Contribution
It introduces new results on global-local mixing for diverse infinite measure systems, including nonMarkovian and multidimensional intermittent maps, and complex parabolic rational maps.
Findings
Proves global-local mixing for intermittent maps with multiple neutral fixed points.
Extends mixing results to nonMarkovian and multidimensional systems.
Includes new results for parabolic rational maps of the complex plane.
Abstract
We prove global-local mixing for a large class of dynamical systems with infinite invariant measure. In particular, we treat intermittent maps including maps with multiple neutral fixed points, nonMarkovian intermittent maps, and multidimensional nonMarkovian intermittent maps. We also prove global-local mixing for parabolic rational maps of the complex plane.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Markov Chains and Monte Carlo Methods · Stability and Controllability of Differential Equations