Dynamic Equivalence: Features and Merits

Equivalence and Dynamic Linearization

This paper presents an (innnite dimensional) geometric framework for control system, based on innnite jet bundles, where a system is represented by a single vector eld and dynamic equivalence (to be precise : equivalence by endogenous dynamic feedback) is conjugation by diieomorphisms. These diieomorphisms are very much related to Lie-BB acklund transformations. It is proved in this framework t...

Dynamic equivalence relation on the fuzzy measure algebras

The main goal of the present paper is to extend classical results from the measure theory and dynamical systems to the fuzzy subset setting. In this paper, the notion of  dynamic equivalence relation is introduced and then it is proved that this relation is an equivalence relation. Also, a new metric on the collection of all equivalence classes is introduced and it is proved that this metric is...

Regular equivalence and dynamic logic

This paper describes a precise linguistic counterpart to the notion of a regular equivalence relation on a social network. That is, a formal language of position terms is defined with the property that on finite networks, two actors are regularly equivalent if and only if they cannot be distinguished by a position term. The paper also contains an exact characterization of the set of complex rel...

A differential geometric setting for dynamic equivalence and dynamic linearization

This paper presents an (infinite dimensional) geometric framework for control system, based on infinite jet bundles, where a system is represented by a single vector field and dynamic equivalence (to be precise : equivalence by endogenous dynamic feedback) is conjugation by diffeomorphisms. These diffeomorphisms are very much related to Lie-Bäcklund transformations. It is proved in this framewo...

Equivalence between Dynamic Neural Networks