AIMR Math Group Seminar 2024/11/29
Date : November. 29th (Fri) 2024 16:00-17:30
Venue: AIMR, 2F Seminar room / Zoom
Speaker: Dr. Shoya Motonaga (Ritsumeikan University)
Title: Upper bounds of the numbers of first integrals and commutative vector fields for nearly integrable systems
Abstract:
In the study of continuous dynamical systems (systems of ordinary differential equations), existence of first integrals (conserved quantities) and commutative vector fields (infinitesimal generators of continuous symmetries) is important since they impose strong constraints on the dynamics. In particular, a system is said to be integrable (in the sense of Bogoyavlenskij) if there are as many functionally independent first integrals and linearly independent commutative vector fields as the dimension of the system, and it is known that the dynamics of integrable systems are very simple. Therefore, the numbers of first integrals and commutative vector fields correspond to some kind of complexity of the system. In this talk, we give upper bounds of the numbers of first integrals and commutative vector fields for nearly integrable systems by using a Melnikov-type function.
*Register here
*The seminar is co-hosted by MathCCS Seminar.
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