| Abstract: |
| The aim of the talk is to discuss the strong relationship between dynamical system and group action on a non-empty set. Let G be a group and X be a non-empty set. The notion of the action of G on the set X is very important in mathematics. If X has also an algebraic structure then such action is more important. For instance, if X is a vector space or a group or a topological structure and so on. The symmetric structure of the notion of groups reflects a lot of behaviours and results which are related to the so-called orbits, stabilizer, fixed points and invariants. On the other hand, dynamical system meets with group action in many places as it studies the evolution and the symmetry for discrete and continuous objects. We believe that the relationship between dynamical systems and algebra is very strong and we are searching in this direction. In this talk, we shall represent examples and environment in which such relationship makes sense and try to envisage common analytical process to exploit this connexion. We shall mention also the relationship between dynamical systems with: ergodic , topology, geometry, logic, numbers, probability, analysis, and category. |
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