Hypercyclic operators for iterated function systems
Mohammad Salman,Ruchi Das +1 more
TL;DR: In this article, the notion of hypercyclicity for iterated function systems (IFS) of operators is introduced and studied, and it is shown that for a linear IFS, hyper-cyclicity implies sensitivity and if an IFS is abelian, then hypercyclity also implies multi-sensitivity and hence thick sensitivity.
read more
Abstract: In this paper we introduce and study the notion of hypercyclicity for iterated function systems (IFS) of operators. We prove that for a linear IFS, hypercyclicity implies sensitivity and if an IFS is abelian, then hypercyclicity also implies multi-sensitivity and hence thick sensitivity. We also give some equivalent conditions for hypercyclicity as well as weakly mixing for an IFS of operators.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Variants of Shadowing Properties for Iterated Function Systems on Uniform Spaces
Radhika Vasisht,Mohammad Salman,Ruchi Das +2 more
TL;DR: This paper introduces and studies variants of shadowing properties for iterated function systems on uniform spaces, establishing relationships between topological shadowing, ergodic shadowing, chain transitivity, and chain mixing, and their implications on ergodicity and transitivity.
References
•Book
Dynamics of Linear Operators
Frédéric Bayart,Etienne Matheron +1 more
- 27 Jul 2009
TL;DR: In this paper, the authors introduce the concept of hypercyclicity everywhere and hypercyclic subspaces and the angle criterion for linear dynamics and the weak topology of the Riemann zeta function.
985
Solving the inverse problem for function/image approximation using iterated function systems i: theoretical basis
Bruno Forte,Edward R. Vrscay +1 more
TL;DR: In this paper, an N-map IFS with grey level maps (IFSM) is proposed, where each IFSM is associated with a contractive operator T with fixed point, and a rigorous solution to the following inverse problem is provided: given a target υ ∈ ℒp(X, µ) and an ∊ > 0, find an IFSm whose attractor satisfies.
48
Shadowing and average shadowing properties for iterated function systems
TL;DR: In this paper, the shadowing and average shadowing properties for iterated function systems are defined and some examples characterizing these definitions are given. And the authors prove that a system has shadowing property if and only if the step skew product corresponding to the system has shadows.
34
•Posted Content
J-class operators and hypercyclicity
TL;DR: In this article, a new notion related to lineardynamics, which can be viewed as a "localization" of the notion of hypercyclicity, is introduced, and the authors investigate the class of operators satisfying the above property and provide various examples.
Iterated function systems a rising from recursive estimation problems
J. H. Elton,M. Piccioni +1 more
TL;DR: In this paper, it was shown that the one-step predictor of a finite-state Markov chain from noisy observations has a unique stationary law which is supported by a self-similar set, called the attractor.
33