Ruchi Das - Academia.edu (original) (raw)

Papers by Ruchi Das

Filomat

In this paper, the interrelations of some dynamical properties of a non-autonomous dynamical syst... more In this paper, the interrelations of some dynamical properties of a non-autonomous dynamical system (X, f1, ?) and its induced non-autonomous dynamical system (K(X), f1, ?) are studied, where K(X) is the hyperspace of all non-empty compact subsets of X, endowed with Vietoris topology. Various stronger forms of sensitivity and transitivity are considered. Some examples of non-autonomous systems are provided to support the results. A relation between shadowing property of the non-autonomous system (X, f1, ?) and its induced system (K(X), f1, ?) is studied.

Journal of Difference Equations and Applications

We study some stronger forms of sensitivity, namely, F-sensitivity and weaklyF-sensitivity for no... more We study some stronger forms of sensitivity, namely, F-sensitivity and weaklyF-sensitivity for non-autonomous discrete dynamical systems. We obtain a condition under which these two forms of sensitivity are equivalent. We also justify the difference between F-sensitivity and some other stronger forms of sensitivity through examples. We explore the relation between the F-sensitivity of the nonautonomous system (X, f1,∞) and autonomous system (X, f), where fn is a sequence of continuous functions converging uniformly to f. We also study the F-sensitivity of a non-autonomous system (X, f1,∞), generated by a finite family of maps F = {f1, f2,. .. , f k } and give an example showing that such non-autonomous systems can be F-sensitive, even when none of the maps in the family F is F-sensitive.

Bulletin of Mathematical Sciences, 2013

In this paper we discuss the dynamical system induced by sequence of maps i.e. time varying map o... more In this paper we discuss the dynamical system induced by sequence of maps i.e. time varying map on a metric space. We define and study shadowing and expansiveness of such dynamical systems. We show that expansiveness and shadowing of time varying maps are conjugacy invariant. Finally, we prove that a time varying map having shadowing and expansiveness is topologically stable in the class of all time varying maps on a compact metric space.

Periodica Mathematica Hungarica, 1995

Beginning with examples, the notion ofG-expansiveness over a metric spaceX on which a topological... more Beginning with examples, the notion ofG-expansiveness over a metric spaceX on which a topological groupG acts is introduced. Some conditions are determined under which expansiveness onX impliesG-expansiveness. A characterization of aG-expansive homeomorphism is obtained which in turn gives a sufficient condition for the homeomorphic extension of aG-expansive homeomorphism to beG-expansive. At the end, some results are stated in the form of concluding remarks.

Applied General Topology, 2016

We prove that if a uniformly continuous self-map fff of a uniform space has topological specifica... more We prove that if a uniformly continuous self-map fff of a uniform space has topological specification property then the map fff has positive uniform entropy, which extends the similar known result for homeomorphisms on compact metric spaces having specification property. An example is also provided to justify that the converse is not true.<br /><br />

Filomat

In this paper, the interrelations of some dynamical properties of a non-autonomous dynamical syst... more In this paper, the interrelations of some dynamical properties of a non-autonomous dynamical system (X, f1, ?) and its induced non-autonomous dynamical system (K(X), f1, ?) are studied, where K(X) is the hyperspace of all non-empty compact subsets of X, endowed with Vietoris topology. Various stronger forms of sensitivity and transitivity are considered. Some examples of non-autonomous systems are provided to support the results. A relation between shadowing property of the non-autonomous system (X, f1, ?) and its induced system (K(X), f1, ?) is studied.

Journal of Difference Equations and Applications

We study some stronger forms of sensitivity, namely, F-sensitivity and weaklyF-sensitivity for no... more We study some stronger forms of sensitivity, namely, F-sensitivity and weaklyF-sensitivity for non-autonomous discrete dynamical systems. We obtain a condition under which these two forms of sensitivity are equivalent. We also justify the difference between F-sensitivity and some other stronger forms of sensitivity through examples. We explore the relation between the F-sensitivity of the nonautonomous system (X, f1,∞) and autonomous system (X, f), where fn is a sequence of continuous functions converging uniformly to f. We also study the F-sensitivity of a non-autonomous system (X, f1,∞), generated by a finite family of maps F = {f1, f2,. .. , f k } and give an example showing that such non-autonomous systems can be F-sensitive, even when none of the maps in the family F is F-sensitive.

Bulletin of Mathematical Sciences, 2013

In this paper we discuss the dynamical system induced by sequence of maps i.e. time varying map o... more In this paper we discuss the dynamical system induced by sequence of maps i.e. time varying map on a metric space. We define and study shadowing and expansiveness of such dynamical systems. We show that expansiveness and shadowing of time varying maps are conjugacy invariant. Finally, we prove that a time varying map having shadowing and expansiveness is topologically stable in the class of all time varying maps on a compact metric space.

Periodica Mathematica Hungarica, 1995

Beginning with examples, the notion ofG-expansiveness over a metric spaceX on which a topological... more Beginning with examples, the notion ofG-expansiveness over a metric spaceX on which a topological groupG acts is introduced. Some conditions are determined under which expansiveness onX impliesG-expansiveness. A characterization of aG-expansive homeomorphism is obtained which in turn gives a sufficient condition for the homeomorphic extension of aG-expansive homeomorphism to beG-expansive. At the end, some results are stated in the form of concluding remarks.

Applied General Topology, 2016

We prove that if a uniformly continuous self-map fff of a uniform space has topological specifica... more We prove that if a uniformly continuous self-map fff of a uniform space has topological specification property then the map fff has positive uniform entropy, which extends the similar known result for homeomorphisms on compact metric spaces having specification property. An example is also provided to justify that the converse is not true.<br /><br />