فهرست مطالب zahra eslami giski

Entropy measures have received considerable attention in quantifying the structural complexity of real-world systems and are also used as measures of information obtained from a realization of the considered experiments. In the present study, new notions of entropy for a dynamical system are introduced. The Rényi entropy of measurable partitions of order and its conditional version are defined, and some important properties of these concepts are studied. It is shown that the Shannon entropy and its conditional version for measurable partitions can be obtained as the limit of their Rényi entropy and conditional Rényi entropy. In addition, using the suggested concept of Rényi entropy for measurable partitions, the Rényi entropy for dynamical systems is introduced. It is also proved that the Rényi entropy for dynamical systems is invariant under isomorphism.

ABSTRAct. In this paper, a relative intuitionistic dynamical system with the levels (α, β), as a mathematical model compatible with a natural phenome- non, is proposed. In addition, the notion of RI topological entropy with the levels (α, β) for RI dynamical systems with the levels (α, β) is defined and its properties are studied. As a significant result, it was shown that, this topolog- ical entropy is an invariant object up to conjugate relation.