Seminar Geometrija i primene, 14. april 2022.

• 11. April,  2022
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Naredni sastanak Seminara biće održan onlajn u četvrtak, 14. aprila 2022, sa početkom u 17.15 preko Webex platforme.

Predavač: Vladislav Kibkalo, Lomonosov Moscow State University

Naslov predavanja: INTEGRABLE SYSTEMS OF DYNAMICS IN PSEUDO-EUCLIDEAN SPACE AND TOPOLOGY OF NON-COMPACT LIOUVILLE FOLIATIONS

Apstrakt:
Finite-dimensional integrable systems obtain a structure of Liouville foliation, i.e. their phase space is a disjoint union of common level surfaces (their connected components) of their integrals. Theory of topological classification of such systems and their singularities was built by A. Fomenko and his school. Integrable systems of rigid body dynamics, e.g. Euler, Lagrange and Kovalevskaya tops were analysed in this way and appeared to realize a lot of interesting effects possible in this theory.

Two properties of foliations important for the classification theorems are the compactness of the fibers (connected common levels of integrals) and completeness of Hamiltonian flows of their integrals (phase trajectory is well-defined for each real time). Extending the topological classification theory to other integrable systems is an open and fundamental problem.

As the first step it can be fruitful to obtain a set of examples of such foliations and analyze them. As it turns out, dynamical systems in a pseudo-Euclidean space (e.g. such analogs of famous integrable tops of Euler, Lagrange and Kovalevskaya) are also integrable and realize foliations with both compact and noncompact fibers and non-critical singularities (i.e. the foliation is not locally trivial but does not contain critical points of first integrals). We will discuss properties of such systems and topology of their Liouville foliations studied by the speaker.

Link za pristup:
https://matf.webex.com/matf/j.php?MTID=m3a137bcce53358200bba0b9a92f2722d
Meeting number (access code): 2405 281 3209
Meeting password: qyWHVf6dS47

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