We investigate the properties of chain recurrent, chain transitive, and chain mixing maps (generalizations of the wellknown notions of non-wandering, topologically transitive, and topologically mixing maps). We describe the structure of chain transitive maps. These notions of recurrence are defined using ε-chains, and the minimal lengths of these ε-chains give a way to measure recurrence time (...

We describe a rigorous and efficient computer algorithm for building a model of the dynamics of a polynomial diffeomorphism of C on its chain recurrent set, R, and for sorting points into approximate chain transitive components. Further, we give explicit estimates which quantify how well this algorithm approximates the chain recurrent set and distinguishes the chain transitive components. We al...

In this paper, the new concept of non-autonomous iterated function system is introduced and also shown that non-autonomous iterated function system IFS(f_(1,∞)^0,f_(1,∞)^1) is topologically transitive for the metric space of X whenever the system has average shadowing property and its minimal points on X are dense. Moreover, such a system is topologically transitive, whenever, there is a point ...

Abstract: An approach to calculate the exact transitive closure of a parameterized and normalized affine integer tuple relation is presented. A relation is normalized when it describes graphs of the chain topology only. A procedure of the normalization is attached. The exact transitive closure calculation is based on resolving a system of recurrence equations being formed from the input and out...

A probabilistic causal chain ABC may intuitively appear to be transitive: If A probabilistically causes B, and B probabilistically causes C, A probabilistically causes C. However, probabilistic causal relations are only transitive if the so-called Markov condition holds. In two experiments, we examined how people make probabilistic judgments about indirect relationships AC in causal chains A...