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 Scijournal_title
Royal Society open scienceauthors
Stadlmann J,Erban Rdoi
10.1098/rsos.191423subject
Has Abstractpub_date
2019-11-27 00:00:00pages
191423issue
11issn
2054-5703pii
rsos191423journal_volume
6pub_type
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