Limiting stochastic processes of shift-periodic dynamical systems.
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ABSTRACT:
SUBMITTER: Stadlmann J
PROVIDER: S-EPMC6894602 | biostudies-literature | 2019 Nov
REPOSITORIES: biostudies-literature
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Limiting stochastic processes of shift-periodic dynamical systems.
Stadlmann Julia J Erban Radek R
Royal Society open science 20191127 11
A shift-periodic map is a one-dimensional map from the real line to itself which is periodic up to a linear translation and allowed to have singularities. It is shown that iterative sequences <i>x</i> <sub><i>n</i>+1</sub> = <i>F</i>(<i>x</i> <sub><i>n</i></sub> ) generated by such maps display rich dynamical behaviour. The integer parts ⌊ x n ⌋ give a discrete-time random walk for a suitable initial distribution of <i>x</i> <sub>0</sub> and converge in certain limits to Brownian motion or more ...[more]
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