Anima Nagar
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View article: Some relations in topological dynamics
Some relations in topological dynamics Open
Relations always play an important role in the study of topological dynamics. Proximal, distal and almost periodic relations are well studied in literature. We further this direction and analogously study the strongly proximal and weakly d…
View article: On almost periodicity and minimality for semiflows
On almost periodicity and minimality for semiflows Open
In topological dynamics, the dynamical behavior sometimes has a sharp\ncontrast when the action is by semigroups or monoids to when the action is by\ngroups. In this article we bring out this contrast while discussing the\nequivalence of a…
View article: BRATTELI–VERSHIKISABILITY OF POLYGONAL BILLIARDS ON THE HYPERBOLIC PLANE
BRATTELI–VERSHIKISABILITY OF POLYGONAL BILLIARDS ON THE HYPERBOLIC PLANE Open
Bratteli–Vershik models of compact, invertible zero-dimensional systems have been well studied. We take up such a study for polygonal billiards on the hyperbolic plane, thus considering these models beyond zero-dimensions. We describe the …
View article: Some Variations of Transitivity for CR-dynamical systems
Some Variations of Transitivity for CR-dynamical systems Open
We consider the topological dynamics of closed relations(CR) by studying one of the oldest dynamical property - `transitivity'. We investigate the two kinds of (closed relation) CR-dynamical systems - $(X,G)$ where the relation $G \subsete…
View article: Finiteness in polygonal billiards on hyperbolic plane
Finiteness in polygonal billiards on hyperbolic plane Open
\textsc{J. Hadamard} studied the geometric properties of geodesic flows on surfaces of negative curvature, thus initiating "Symbolic Dynamics". In this article, we follow the same geometric approach to study the geodesic trajectories of bi…
View article: On Almost periodicity and minimality for semiflows
On Almost periodicity and minimality for semiflows Open
In topological dynamics, the dynamical behavior sometimes has a sharp contrast when the action is by semigroups or monoids to when the action is by groups. In this article we bring out this contrast while discussing the equivalence of almo…
View article: Rendezvous with sensitivity
Rendezvous with sensitivity Open
Let $(X,d)$ be a compact metric space and $f:X \\to X$ be a self-map. The\ncompact dynamical system $(X,f)$ is called sensitive or sensitivity depends on\ninitial conditions, if there is a positive constant $\\delta$ such that in each\nnon…
View article: Topological Dynamics of Enveloping Semigroups
Topological Dynamics of Enveloping Semigroups Open
A compact metric space $X$ and a discrete topological acting group $T$ give a flow $(X,T)$. Robert Ellis had initiated the study of dynamical properties of the flow $(X,T)$ via the algebraic properties of its "Enveloping Semigroup" $E(X)$.…
View article: Dynamics of the Induced Shift Map
Dynamics of the Induced Shift Map Open
In this article, we compare the dynamics of the shift map and its induced counterpart on the hyperspace of the shift space. We show that many of the properties of induced shift map can be easily demonstrated by appropriate sequences of sym…
View article: Variations on the concept of topological transitivity
Variations on the concept of topological transitivity Open
We describe various strengthenings of the concept of topological transitivity. Especially when one departs from the family of invertible systems, a number of interesting properties arise. We present the architecture of implications among t…