New semi-Hamiltonian hierarchy related to integrable magnetic flows on surfaces

Misha Bialy; Andrey Mironov

doi:10.2478/s11533-012-0045-3

New semi-Hamiltonian hierarchy related to integrable magnetic flows on surfaces

Misha Bialy, Andrey Mironov

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

We consider magnetic geodesic flows on the two-torus. We prove that the question of existence of polynomial in momenta first integrals on one energy level leads to a semi-Hamiltonian system of quasi-linear equations, i. e. in the hyperbolic regions the system has Riemann invariants and can be written in conservation laws form.

Original language	English
Pages (from-to)	1596-1604
Number of pages	9
Journal	Central European Journal of Mathematics
Volume	10
Issue number	5
DOIs	https://doi.org/10.2478/s11533-012-0045-3
State	Published - Oct 2012

Keywords

Integral of motion
Magnetic geodesic flows
Riemann invariants
Systems of hydrodynamic type

All Science Journal Classification (ASJC) codes

General Mathematics

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10.2478/s11533-012-0045-3

Cite this

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title = "New semi-Hamiltonian hierarchy related to integrable magnetic flows on surfaces",

abstract = "We consider magnetic geodesic flows on the two-torus. We prove that the question of existence of polynomial in momenta first integrals on one energy level leads to a semi-Hamiltonian system of quasi-linear equations, i. e. in the hyperbolic regions the system has Riemann invariants and can be written in conservation laws form.",

keywords = "Integral of motion, Magnetic geodesic flows, Riemann invariants, Systems of hydrodynamic type",

author = "Misha Bialy and Andrey Mironov",

note = "Funding Information: Misha Bialy was supported in part by the Israel Science Foundation grant 128/10 and Andrey Mironov was supported by RFBR grant 11-01-12106-ofi-m-2011.",

year = "2012",

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doi = "10.2478/s11533-012-0045-3",

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N2 - We consider magnetic geodesic flows on the two-torus. We prove that the question of existence of polynomial in momenta first integrals on one energy level leads to a semi-Hamiltonian system of quasi-linear equations, i. e. in the hyperbolic regions the system has Riemann invariants and can be written in conservation laws form.

AB - We consider magnetic geodesic flows on the two-torus. We prove that the question of existence of polynomial in momenta first integrals on one energy level leads to a semi-Hamiltonian system of quasi-linear equations, i. e. in the hyperbolic regions the system has Riemann invariants and can be written in conservation laws form.

KW - Integral of motion

KW - Magnetic geodesic flows

KW - Riemann invariants

KW - Systems of hydrodynamic type

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DO - 10.2478/s11533-012-0045-3

M3 - مقالة

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JO - Central European Journal of Mathematics

JF - Central European Journal of Mathematics

IS - 5

ER -

New semi-Hamiltonian hierarchy related to integrable magnetic flows on surfaces

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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