COADJOINT ORBITS OF SYMPLECTIC DIFFEOMORPHISMS OF SURFACES AND IDEAL HYDRODYNAMICS

Izosimov Anton; Khesin Boris; Mousavi Mehdi

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COADJOINT ORBITS OF SYMPLECTIC DIFFEOMORPHISMS OF SURFACES AND IDEAL HYDRODYNAMICS

机译：COADJOINT ORBITS OF SYMPLECTIC DIFFEOMORPHISMS OF SURFACES AND IDEAL HYDRODYNAMICS

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摘要

We give a classification of generic coadjoint orbits for the groups of symplectomorphisms and Hamiltonian diffeomorphisms of a closed symplectic surface. We also classify simple Morse functions on symplectic surfaces with respect to actions of those groups. This gives an answer to V. Arnold's problem on describing all invariants of generic isovorticed fields for the 2D ideal fluids. For this we introduce a notion of anti-derivatives on a measured Reeb graph and describe their properties.

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来源
《Annales de l'Institut Fourier》 |2016年第6期|2385-2433|共49页
作者
Izosimov Anton; Khesin Boris; Mousavi Mehdi;
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作者单位

Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada;

Univ Western Ontario, Dept Stat & Actuarial Sci, London, ON N6A 5B7, Canada;

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正文语种英语
中图分类自然科学总论;
关键词
coadjoint orbits; symplectic diffeomorphisms; Hamiltonian diffeomorphisms; Casimirs; simple Morse functions; isovorticed fields; measured Reeb graphs; pants decomposition; vorticity function; circulations;

COADJOINT ORBITS OF SYMPLECTIC DIFFEOMORPHISMS OF SURFACES AND IDEAL HYDRODYNAMICS

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