Saddle Singularities in Integrable Hamiltonian Systems: Examples and Algorithms

Авторы: Fomenko A.T., Kibkalo V.A.
Сборник: Sadovnichiy V.A., Zgurovsky M.Z. (eds). Contemporary Approaches and Methods in Fundamental Mathematics and Mechanics
Серия: Understanding Complex Systems
Год издания: 2021
Место издания: Springer, Cham Switzerland
Первая страница: 3
Последняя страница: 26
DOI: 10.1007/978-3-030-50302-4_1
Аннотация: Saddle or hyperbolic singularities of Liouville foliations of integrable Hamiltonian systems are discussed. We observe new and classical results on their classification, representation and invariants with respect to topological equivalence depending on number of degrees of freedom. Then criterion of their component-wise stability by A.A.~Oshemkov and its application are reminded. At last, we discuss saddle singularities of famous dynamical and physical systems, particularly problem of realization (modeling) of Liouville foliations and their singularities (A.T.~Fomenko billiard conjecture) by integrable billiards. New result is obtained: loop molecules of all saddle-saddle singularities with one equilibria are modeled by billiard books, i.e. integrable billiards on CW-complexes introduced by V.V.~Vedyushkina.
Добавил в систему: Кибкало Владислав Александрович

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