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Shadowing and average shadowing properties for iterated function systems
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Alireza Zamani Bahabadi
Published/Copyright:
April 2, 2015
Abstract
In this paper, we introduce the definitions of shadowing and average shadowing properties for iterated function systems and give some examples characterizing these definitions. We prove that an iterated function system has the shadowing property if and only if the step skew product corresponding to the iterated function system has the shadowing property. Also, we study some notions such as transitivity, chain transitivity, chain mixing and mixing for iterated function systems.
Keywords: Shadowing property; average shadowing property; iterated function systems; transitivity; mixing
The author would like to take this opportunity to express his thanks to Sergey Tikhomirov for useful discussions.
Received: 2013-6-25
Revised: 2014-1-29
Accepted: 2014-4-21
Published Online: 2015-4-2
Published in Print: 2015-6-1
© 2015 by De Gruyter
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Keywords for this article
Shadowing property;
average shadowing property;
iterated function systems;
transitivity;
mixing
Articles in the same Issue
- Frontmatter
- I2(u)-convergence of double sequences of order (α,β)
- Regular elements of the complete semigroups of binary relations of the class Σ6(X,8)
- On the limit properties of maximal likelihood estimators in a Hilbert space
- Shadowing and average shadowing properties for iterated function systems
- On almost increasing and quasi monotone sequences
- An unabelian version of the Voronov higher bracket construction
- Necessary and sufficient conditions for the ℍ-differentiability of quaternion functions
- k-step nilpotent Lie algebras
- An optimal control problem for a system of linear hyperbolic differential equations with constant coefficients
- On topologies in the family of sets with the Baire property
- On some inequalities for functions whose absolute values of the second derivatives are α-, m-, (α,m)-logarithmically convex
- On the cardinalities of at-sets in a real Hilbert space
- Higher-order Bernoulli and poly-Bernoulli mixed type polynomials
- On the existence of solutions for nonlocal boundary value problems
- fpn-injective and fpn-flat modules
- Algebroid functions with given Borel points
