Abstract
AbstractBassed on the intrinsic structure of a selfmapping T: S → S of an arbitrary set S, called the orbit-structure of T, a new entropy is defined. The idea is to use the number of preimages of an element x under the iterates of T to characterize the complexity of the transformation T and their orbit graphs. The fundamental properties of the orbit entropy related to iteration, iterative roots and iteration semigroups are studied. For continuous (differentiable) functions of Rn to Rn, the chaos of Li and Yorke is characterized by means of this entropy, mainly using the method of Straffingraphs.
Publisher
Cambridge University Press (CUP)
Subject
General Mathematics,Statistics and Probability
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