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 x n+1 = F(x n ) generated by such maps display rich dynamical behaviour. The integer parts ⌊xn⌋ give a discrete-time random walk for a suitable initial distribution of x 0 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.

SUBMITTER: Stadlmann J 

PROVIDER: S-EPMC6894602 | biostudies-literature | 2019 Nov

REPOSITORIES: biostudies-literature