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Trajectories, first return limiting notions and rings of H -connected and iteratively H -connected functions

Ewa Korczak-Kubiak, Ryszard J. Pawlak (2013)

Czechoslovak Mathematical Journal

In the paper the existing results concerning a special kind of trajectories and the theory of first return continuous functions connected with them are used to examine some algebraic properties of classes of functions. To that end we define a new class of functions (denoted C o n n * ) contained between the families (widely described in literature) of Darboux Baire 1 functions ( DB 1 ) and connectivity functions ( C o n n ). The solutions to our problems are based, among other, on the suitable construction of the ring,...

Trajectory of the turning point is dense for a co-σ-porous set of tent maps

Karen Brucks, Zoltán Buczolich (2000)

Fundamenta Mathematicae

It is known that for almost every (with respect to Lebesgue measure) a ∈ [√2,2] the forward trajectory of the turning point of the tent map T a with slope a is dense in the interval of transitivity of T a . We prove that the complement of this set of parameters of full measure is σ-porous.

Transitive flows on manifolds.

Víctor Jiménez López, Gabriel Soler López (2004)

Revista Matemática Iberoamericana

In this paper we characterize manifolds (topological or smooth, compact or not, with or without boundary) which admit flows having a dense orbit (such manifolds and flows are called transitive) thus fully answering some questions by Smith and Thomas. Name

Ultrafilter-limit points in metric dynamical systems

Salvador García-Ferreira, Manuel Sanchis (2007)

Commentationes Mathematicae Universitatis Carolinae

Given a free ultrafilter p on ℕ and a space X , we say that x ∈ X is the p -limit point of a sequence ( x n ) n ∈ ℕ in X (in symbols, x = p - lim n → ∞ x n ) if for every neighborhood V of x , { n ∈ ℕ : x n ∈ V } ∈ p . By using p -limit points from a suitable metric space, we characterize the selective ultrafilters on ℕ and the P -points of ℕ * = β ( ℕ ) ∖ ℕ . In this paper, we only consider dynamical systems ( X , f ) , where X is a compact metric space. For a free ultrafilter p on ℕ * , the function f p : X → X is defined by f p ( x ) = p - lim n → ∞ f n ( x ) for each x ∈ X . These functions are not continuous in general. For a...

Uncountable ω-limit sets with isolated points

Chris Good, Brian E. Raines, Rolf Suabedissen (2009)

Fundamenta Mathematicae

We give two examples of tent maps with uncountable (as it happens, post-critical) ω-limit sets, which have isolated points, with interesting structures. Such ω-limit sets must be of the form C ∪ R, where C is a Cantor set and R is a scattered set. Firstly, it is known that there is a restriction on the topological structure of countable ω-limit sets for finite-to-one maps satisfying at least some weak form of expansivity. We show that this restriction does not hold if the ω-limit set is uncountable....

Une version feuilletée équivariante du théorème de translation de Brouwer

Patrice Le Calvez (2005)

Publications Mathématiques de l'IHÉS

The Brouwer’s plane translation theorem asserts that for a fixed point free orientation preserving homeomorphism f of the plane, every point belongs to a Brouwer line: a proper topological embedding C of R, disjoint from its image and separating f(C) and f–1(C). Suppose that f commutes with the elements of a discrete group G of orientation preserving homeomorphisms acting freely and properly on the plane. We will construct a G-invariant topological foliation of the plane by Brouwer lines. We apply...

Uniformly recurrent sequences and minimal Cantor omega-limit sets

Lori Alvin (2015)

Fundamenta Mathematicae

We investigate the structure of kneading sequences that belong to unimodal maps for which the omega-limit set of the turning point is a minimal Cantor set. We define a scheme that can be used to generate uniformly recurrent and regularly recurrent infinite sequences over a finite alphabet. It is then shown that if the kneading sequence of a unimodal map can be generated from one of these schemes, then the omega-limit set of the turning point must be a minimal Cantor set.

Universal minimal dynamical system for reals

Sławomir Turek (1995)

Commentationes Mathematicae Universitatis Carolinae

Our aim is to give a description of S ( ℝ ) and M ( ℝ ) , the phase space of universal ambit and the phase space of universal minimal dynamical system for the group of real numbers with the usual topology.

Currently displaying 441 – 460 of 523