Related papers: Topological conjugacy for unimodal nonautonomous d…
The purpose of this article is to study the relation between combinatorial equivalence and topological conjugacy, specifically how a certain type of combinatorial equivalence implies topological conjugacy. We introduce the concept of…
Topological conjugateness of one dimensional unimodal dynamical systems, which are generated by interval [0, 1] into itself maps are studied. We study the smoothness and differentiability of the conjugacy of symmetrical and non-symmetrical…
We consider tiling dynamical systems and topological conjugacies between them. We prove that the criterion of being finite type is invariant under topological conjugacy. For substitution tiling systems under rather general conditions,…
This paper explores the concept of topological transitivity in nonautonomous dynamical systems, which are defined as sequences of continuous maps from a compact metric space to itself. It investigates various conditions (including…
We present sufficient conditions under which a given linear nonautonomous system and its nonlinear perturbation are topologically conjugated. Our conditions are of a very general form and provided that the nonlinear perturbations are…
This work describes the way that topological mixing and chaos in continua, as induced by discrete dynamical systems, can or can't be understood through topological conjugacy with symbolic dynamical systems. For example, there is no symbolic…
Recently a new class of critical points, termed as {\sl perpetual points}, where acceleration becomes zero but the velocity remains non-zero, is observed in nonlinear dynamical systems. In this work we show whether a transformation also…
Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity.…
This paper establishes topological (equi-)semiconjugacy and (equi-)conjugacy between induced non-autonomous set-valued systems and subshifts of finite type. First, some necessary and sufficient conditions are given for a non-autonomous…
The aim of this paper is to give a condition to topological conjugacy of invariant flows in an Lie group $G$ which its Lie algebra $\mathfrak{g}$ is associative algebra or semisimple. In fact, we show that if two dynamical system on $G$ are…
We characterize the symbolical dynamical systems which are topologically isomorphic to the Fibonacci dynmaical system. We prove that there are infinitely many injective primitive substitutions generating a dynamical system in the Fibonacci…
In this paper we study topological entropy and recurrence properties of non-autonomous dynamical system generated by a family of continuous self maps on a compact space X. Specially, we introduce the pseudo-entropy and…
We resolve the isomorphism problem for tensor algebras of unital multivariable dynamical systems. Specifically we show that unitary equivalence after a conjugation for multivariable dynamical systems is a complete invariant for complete…
The topological classification of the inner mappings on the fully invariant regular components of the wandering set with a special attracting boundary up to the topological conjugacy is defined in terms of distinguishing graph. Two inner…
We consider the general model for dynamical systems defined on a simplicial complex. We describe the conjugacy classes of these systems and show how symmetries in a given simplicial complex manifest in the dynamics defined thereon,…
The celebrated Takens' embedding theorem concerns embedding an attractor of a dynamical system in a Euclidean space of appropriate dimension through a generic delay-observation map. The embedding also establishes a topological conjugacy. In…
This paper considers a problem of testing, from a finite sample, a topological conjugacy of two dynamical systems $(X,f)$ and $(Y,g)$. More precisely, given $x_1,\ldots, x_n \subset X$ and $y_1,\ldots,y_n \subset Y$ such that $x_{i+1} =…
We take the first steps towards a better understanding of continuous orbit equivalence, i.e., topological orbit equivalence with continuous cocycles. First, we characterise continuous orbit equivalence in terms of isomorphisms of C*-crossed…
We find necessary and sufficient conditions for a dynamical system to be topologically conjugate to any given substitution minimal system, thus extending the results in [CKL] for the Morse and Toeplitz substitutions.
We establish necessary and sufficient conditions for a dynamical system to be topologically conjugate to the Morse minimal set, the shift orbit closure of the Morse sequence, and conditions for topological conjugacy to the closely related…