Related papers: On two recurrence problems
We find new bi-Lipschitz invariants for functions of two complex variables.
Based on a question raised by N. Feldman we discuss the dynamics of tuples of upper triangular Toeplitz matrices over $\mathbb{C}$. Some open problems are posed.
We study planar flows without non-wandering points and prove several properties of these flows in relation with their prolongational relation. The main results of this article are that a planar (regular) wandering flow has no generalized…
This article is meant as a mathematical appendix or comment on [BT]. We first consider the notion of transcritical bifurcations of fixed points of general area-preserving maps, and then adress some questions related to [BT] on bifurcation…
A speedup, like a time change in discrete time dynamics, is a way of moving faster through the orbits of a dynamical system. Linearly recurrence is a stronger form of minimality for subshifts, shared by e.g.\ all primitive substitution…
This paper is devoted to problems stated by Z. Zhou and F. Li in 2009. They concern relations between almost periodic, weakly almost periodic, and quasi-weakly almost periodic points of a continuous map f and its topological entropy. The…
Poincare's last geometric theorem (Poincare-Birkhoff Theorem) states that any area-preserving twist map of annulus has at least two fixed points. We replace the area-preserving condition with a weaker intersection property, which states…
We use the theory of $x-y$ duality to propose a new definition / construction for the correlation differentials of topological recursion; we call it "generalized topological recursion". This new definition coincides with the original…
This paper studies topological definitions of chain recurrence and shadowing for continuous endomorphisms of topological groups generalizing the relevant concepts for metric spaces. It is proved that in this case the sets of chain recurrent…
In order to simulate observational and experimental situations, we consider a leak in the phase space of a chaotic dynamical system. We obtain an expression for the escape rate of the survival probability applying the theory of transient…
Statistical Topology emerged since topological aspects continue to gain importance in many areas of physics. It is most desirable to study topological invariants and their statistics in schematic models that facilitate the identification of…
The mechanism of the exponential transient statistics of Poincar\'e recurrences in the presence of chaos border with its critical structure is studied using two simple models: separatrix map and the kicked rotator ('microtron'). For the…
We study conditions under which a space that has a good property and a courser topology with another good property admits a continuous bijection onto a space with both properties.
We consider 9 natural tightness conditions for topological spaces that are all variations on countable tightness and investigate the interrelationships between them. Several natural open problems are raised.
Dynamics near the grazing manifold and basins of attraction for a motion of a material point in a gravitational field, colliding with a moving motion-limiting stop, are investigated. The Poincare map, describing evolution from an impact to…
The last decade has witnessed a number of important and exciting developments that had been achieved for improving recurrence plot based data analysis and to widen its application potential. We will give a brief overview about important and…
In this article, we approach the Arnold corank problem, posed by Arnold in 1975, which asks whether the corank of holomorphic functions is an ambient topological invariant. Here, we obtain a complete positive answer to the metric Arnold…
In this paper we study quantitative recurrence and the shrinking target problem for dynamical systems coming from overlapping iterated function systems. Such iterated function systems have the important property that a point often has…
A key issue in complex systems regards the relationship between topology and dynamics. In this work, we use a recently introduced network property known as steering coefficient as a means to approach this issue with respect to different…
Logical theories have been developed which have allowed temporal reasoning about eventualities (a la Galton) such as states, processes, actions, events, processes and complex eventualities such as sequences and recurrences of other…