There arc uncountably many homeomorphism types of orbits in flows
Toeplitz flows with pure point spectrum
We construct strictly ergodic 0-1 Toeplitz flows with pure point spectrum and irrational eigenvalues. It is also shown that the property of being regular is not a measure-theoretic invariant for strictly ergodic Toeplitz flows.
Topics on analytic sets
Topología grassmaniana sobre los ideales cerrados de codimensión finita de un álgebra de Banach conmutativa.
Topological Affine Spaces and Dynamical Systems
Topological and approximation methods of degree theory of set-valued maps [Book]
Topological aspects of q-regular measures
Topological conditional entropy
Topological conditions for the existence of fixed points
Topological conjugacy of Morse flows over finite Abelian groups
Topological contraction principle
Topological degree and Sperner's lemma
Topological degree theory in fuzzy metric spaces
The aim of this paper is to modify the theory to fuzzy metric spaces, a natural extension of probabilistic ones. More precisely, the modification concerns fuzzily normed linear spaces, and, after defining a fuzzy concept of completeness, fuzzy Banach spaces. After discussing some properties of mappings with compact images, we define the (Leray-Schauder) degree by a sort of colimit extension of (already assumed) finite dimensional ones. Then, several properties of thus defined concept are proved....
Topological disjointness from entropy zero systems
The properties of topological dynamical systems which are disjoint from all minimal systems of zero entropy, , are investigated. Unlike the measurable case, it is known that topological -systems make up a proper subset of the systems which are disjoint from . We show that has an invariant measure with full support, and if in addition is transitive, then is weakly mixing. A transitive diagonal system with only one minimal point is constructed. As a consequence, there exists a thickly syndetic...
Topological dynamics and the extension of Lyapunov's method
Topological Dynamics of Transformations Induced on the Space of Probability Measures.
Topological dynamics of unordered Ramsey structures
We investigate the connections between Ramsey properties of Fraïssé classes and the universal minimal flow of the automorphism group of their Fraïssé limits. As an extension of a result of Kechris, Pestov and Todorcevic (2005) we show that if the class has finite Ramsey degree for embeddings, then this degree equals the size of . We give a partial answer to a question of Angel, Kechris and Lyons (2014) showing that if is a relational Ramsey class and is amenable, then admits a unique invariant...
Topological Entropy and Homology
Topological entropy of nonautonomous piecewise monotone dynamical systems on the interval
The topological entropy of a nonautonomous dynamical system given by a sequence of compact metric spaces and a sequence of continuous maps , , is defined. If all the spaces are compact real intervals and all the maps are piecewise monotone then, under some additional assumptions, a formula for the entropy of the system is obtained in terms of the number of pieces of monotonicity of . As an application we construct a large class of smooth triangular maps of the square of type and positive...
Topological entropy on zero-dimensional spaces
Let X be an uncountable compact metrizable space of topological dimension zero. Given any a ∈[0,∞] there is a homeomorphism on X whose topological entropy is a.