Local and semi-local bifurcations in Hamiltonian dynamical systems

Heinz Hanssmann

Springer Verlag

2020

237 páginas

7h 54m

ISBN-13: 9783540388944

This book demonstrates that while elliptic and hyperbolic tori determine the distribution of maximal invariant tori, they themselves form n-parameter families. Therefore, torus bifurcations of high co-dimension may be found in a single given Hamiltonian system, absent untypical conditions or external parameters. The text moves logically from the integrable case, in which symmetries allow for reduction to bifurcating equilibria, to non-integrability, where smooth parametrisations must be replaced by Cantor sets.