Limiting stochastic processes of shift-periodic dynamical systems
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...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Royal Society
2019
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| _version_ | 1797087541530198016 |
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| author | Stadlmann, J Erban, R |
| author_facet | Stadlmann, J Erban, R |
| author_sort | Stadlmann, J |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T02:37:05Z |
| format | Journal article |
| id | oxford-uuid:a9276fb3-5cfc-419f-8baf-a2541a1d0ff9 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:37:05Z |
| publishDate | 2019 |
| publisher | Royal Society |
| record_format | dspace |
| spelling | oxford-uuid:a9276fb3-5cfc-419f-8baf-a2541a1d0ff92022-03-27T03:06:36ZLimiting stochastic processes of shift-periodic dynamical systemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a9276fb3-5cfc-419f-8baf-a2541a1d0ff9EnglishSymplectic Elements at OxfordRoyal Society2019Stadlmann, JErban, RA 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. |
| spellingShingle | Stadlmann, J Erban, R Limiting stochastic processes of shift-periodic dynamical systems |
| title | Limiting stochastic processes of shift-periodic dynamical systems |
| title_full | Limiting stochastic processes of shift-periodic dynamical systems |
| title_fullStr | Limiting stochastic processes of shift-periodic dynamical systems |
| title_full_unstemmed | Limiting stochastic processes of shift-periodic dynamical systems |
| title_short | Limiting stochastic processes of shift-periodic dynamical systems |
| title_sort | limiting stochastic processes of shift periodic dynamical systems |
| work_keys_str_mv | AT stadlmannj limitingstochasticprocessesofshiftperiodicdynamicalsystems AT erbanr limitingstochasticprocessesofshiftperiodicdynamicalsystems |