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.Keywords Expansiveness · Shadowing · Conjugacy · Topological stability Mathematics Subject Classification (2010) Primary 54H20; Secondary 37C75 · 37C15 IntroductionExpansiveness and shadowing are very important and useful dynamical properties of maps on metric spaces. They have lots of applications in Topological dynamics, Ergodic theory, Symbolic dynamics and related areas. One can refer [2,20] for detailed study of these notions. The concept of expansiveness originally introduced for homeomorphisms on metric spaces [24]

We define and study expansiveness, shadowing, and topological stability for a nonautonomous discrete dynamical system induced by a sequence of homeomorphisms on a metric space.

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In this paper, we study nonwandering set and recurrent set for the non-autonomous discrete dynamical system given by a sequence {f n } ∞ n=0 of homeomorphisms on a compact metric space.

Two homologous series of naphthalene derivatives have been synthesized and the mesomorphic behaviour of their members has been studied. In series I the first nine members are enantiotropic nematic, the decyl derivative edubits a reentrant nematic phase and enantiotropic smectic and nematic phases while the remaining members are enantiotropic smectic. In series I1 the first seven members exhibit nematic, the octyl derivative exhibits monotropic smectic and enantiotropic nematic phases and the remaining members are enantiotropic smectic and nematic or only smectic. The thermal stability of these series is compared with the corresponding homologous series of coumarin derivatives.