Limiting stochastic processes of shift-periodic dynamical systems.

Abstract:

: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 xn+1 = F(x n ) 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 x0 and converge in certain limits to Brownian motion or more general Lévy processes. Furthermore, for certain shift-periodic maps with small holes on [0,1], convergence of trajectories to a continuous-time random walk is shown in a limit.

journal_name

R Soc Open Sci

authors

Stadlmann J,Erban R

doi

10.1098/rsos.191423

subject

Has Abstract

pub_date

2019-11-27 00:00:00

pages

191423

issue

11

issn

2054-5703

pii

rsos191423

journal_volume

6

pub_type

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