Journal article
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(xn) generated by such maps display rich dynamical behaviour. The integer parts ⌊xn⌋ 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.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Publisher copy:
- 10.1098/rsos.191423
Authors
- Publisher:
- Royal Society
- Journal:
- Royal Society Open Science More from this journal
- Volume:
- 6
- Issue:
- 11
- Article number:
- 191423
- Publication date:
- 2019-11-27
- Acceptance date:
- 2019-10-28
- DOI:
- EISSN:
-
2054-5703
- Language:
-
English
- Keywords:
- Pubs id:
-
pubs:943949
- UUID:
-
uuid:a9276fb3-5cfc-419f-8baf-a2541a1d0ff9
- Local pid:
-
pubs:943949
- Source identifiers:
-
943949
- Deposit date:
-
2019-11-10
Terms of use
- Copyright holder:
- Stadlmann and Erban
- Copyright date:
- 2019
- Rights statement:
- © 2019 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
- Licence:
- CC Attribution (CC BY)
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