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5.0

Jun 29, 2018
06/18

by
A. Ehsani; A. Fakhari; F. H. Ghane; M. Zaj

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In this paper we address the existence and ergodicity of non-hyperbolic attracting sets for a certain class of smooth endomorphisms on the solid torus. Such systems allow a formulation as a skew product system defined by planar diffeomorphisms have contraction on average which forced by any expanding circle map. These attractors are invariant graphs of upper semicontinuous maps which support exactly one $SRB$ measure. In our approach, these skew product systems arising from iterated function...

Topics: Dynamical Systems, Mathematics

Source: http://arxiv.org/abs/1606.07322

5
5.0

Jun 29, 2018
06/18

by
F. H. Ghane; E. Rezaali; M. Saleh; A. Sarizadeh

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The present work is concerned with sensitivity of iterated function systems (IFSs). First of all, several sufficient conditions for sensitivity of IFSs are presented. Moreover, we introduce the concept of S-transitivity for IFSs which is relevant with sensitive dependence on initial condition. That yields to a different example of non-minimal sensitive system which is not an M-system. Also, some interesting examples are given which provide some facts about the sensitive property of IFSs

Topics: Dynamical Systems, Mathematics

Source: http://arxiv.org/abs/1603.08243

16
16

Jun 28, 2018
06/18

by
Pablo G. Barrientos; F. H. Ghane; Dominique Malicet; A. Sarizadeh

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Every attractor of an iterated function system (IFS) of continuous functions on a first-countable Hausdorff topological space satisfies the probabilistic chaos game. By contrast, we prove that the backward minimality is a necessary condition to get the deterministic chaos game. We obtain that an IFS of homeomorphisms of the circle satisfies the deterministic chaos game if and only if it is forward and backward minimal. This provides examples of attractors that do not satisfy the deterministic...

Topics: Dynamical Systems, Mathematics

Source: http://arxiv.org/abs/1506.07101