Topologically mixing and minimal but not ergodic, analytic transformation onT 5

2000 ◽  
Vol 31 (3) ◽  
pp. 277-285 ◽  
Author(s):  
Bassam R. Fayad
Keyword(s):  
Analytic Transformation ◽  
Topologically Mixing

Forming mathematical models of electrical circuits by applying analytic transformation

Cybernetics ◽  
1981 ◽  
Vol 17 (2) ◽  
pp. 223-229
Author(s):  
A. I. Petrenko ◽  
G. A. Matrosova
Keyword(s):  
Mathematical Models ◽  
Electrical Circuits ◽  
Analytic Transformation

scholarly journals Topologically Mixing Maps and the Pseudoarc

2014 ◽  
Vol 66 (2) ◽  
pp. 197-208
Author(s):  
T. Drwiega ◽  
P. Oprocha
Keyword(s):  
Topologically Mixing

scholarly journals Topologically mixing hypercyclic operators

2003 ◽  
Vol 132 (2) ◽  
pp. 385-389 ◽  
Author(s):  
George Costakis ◽  
Martín Sambarino
Keyword(s):  
Hypercyclic Operators ◽  
Topologically Mixing

scholarly journals Circle diffeomorphisms forced by expanding circle maps

2011 ◽  
Vol 32 (6) ◽  
pp. 2011-2024 ◽  
Author(s):  
ALE JAN HOMBURG
Keyword(s):  
Natural Extension ◽  
Skew Product ◽  
Circle Maps ◽  
Expanding Circle ◽  
Topologically Mixing ◽  
Almost All ◽  
Open Class ◽  
Product Maps ◽  
Circle Diffeomorphisms

AbstractWe discuss the dynamics of skew product maps defined by circle diffeomorphisms forced by expanding circle maps. We construct an open class of such systems that are robustly topologically mixing and for which almost all points in the same fiber converge under iteration. This property follows from the construction of an invariant attracting graph in the natural extension, a skew product of circle diffeomorphisms forced by a solenoid homeomorphism.

Refined scales of weak-mixing dynamical systems: typical behaviour

2019 ◽  
Vol 40 (12) ◽  
pp. 3296-3309
Author(s):  
SILAS L. CARVALHO ◽  
CÉSAR R. DE OLIVEIRA
Keyword(s):  
Invariant Measures ◽  
Dynamical Behaviour ◽  
Lebesgue Spaces ◽  
Weak Mixing ◽  
Axiom A ◽  
Typical Behaviour ◽  
Topologically Mixing ◽  
Continuous Measures ◽  
Basic Sets ◽  
Measure Preserving Transformations

We study sets of measure-preserving transformations on Lebesgue spaces with continuous measures taking into account extreme scales of variations of weak mixing. It is shown that the generic dynamical behaviour depends on subsequences of time going to infinity. We also present corresponding generic sets of (probability) invariant measures with respect to topological shifts over finite alphabets and Axiom A diffeomorphisms over topologically mixing basic sets.

Hypercyclic, mixing, and chaotic C0-semigroups induced by semiflows

2007 ◽  
Vol 27 (5) ◽  
pp. 1599-1631 ◽  
Author(s):  
T. KALMES
Keyword(s):  
Composition Operators ◽  
Continuous Functions ◽  
Weighted Composition Operators ◽  
Integrable Functions ◽  
Spaces Of Continuous Functions ◽  
Weighted Composition ◽  
Topologically Mixing

AbstractWe characterize when C0-semigroups induced by semiflows are hypercyclic, topologically mixing, or chaotic both on spaces of integrable functions and on spaces of continuous functions. Furthermore, we give characterizations of transitivity for weighted composition operators on these spaces.

Some counterexamples in topological dynamics

2008 ◽  
Vol 28 (4) ◽  
pp. 1291-1322 ◽  
Author(s):  
RONNIE PAVLOV
Keyword(s):  
Topological Dynamics ◽  
Residual Set ◽  
Topologically Mixing ◽  
Uniquely Ergodic

AbstractIn this paper, we exhibit, for any sparse-enough increasing sequence {pn} of integers, totally minimal, totally uniquely ergodic, and topologically mixing systems (X,T) and (X′,T′) and f∈C(X) for which the averages $({1}/{N}) \sum _{n=0}^{N-1} f(T^{p_n} x)$ fail to converge on a residual set in X, and where there exists x′∈X′ with $x' \notin \overline {\{T'^{p_n} x'\}}$.

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