Polynomial integrals of magnetic geodesic flows on the 2-torus on several energy levels

Sergei Agapov; Alexandr Valyuzhenich

doi:10.3934/dcds.2019285

Polynomial integrals of magnetic geodesic flows on the 2-torus on several energy levels

Sergei Agapov, Alexandr Valyuzhenich

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

2 Citations (Scopus)

Abstract

In this paper the geodesic flow on the 2-torus in a non-zero magnetic field is considered. Suppose that this flow admits an additional first integral F on N + 2 different energy levels which is polynomial in momenta of an arbitrary degree N with analytic periodic coefficients. It is proved that in this case the magnetic field and the metric are functions of one variable and there exists a linear in momenta first integral on all energy levels.

Original language	English
Pages (from-to)	6565-6583
Number of pages	19
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	39
Issue number	11
DOIs	https://doi.org/10.3934/dcds.2019285
Publication status	Published - Nov 2019

Keywords

Magnetic geodesic flow, polynomial first integrals
QUASI-LINEAR SYSTEM
1ST INTEGRALS
HAMILTONIAN-SYSTEMS
RIGIDITY
Magnetic geodesic flow
MECHANICAL SYSTEM
polynomial first integrals

OECD FOS+WOS

1.01 MATHEMATICS

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10.3934/dcds.2019285

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abstract = "In this paper the geodesic flow on the 2-torus in a non-zero magnetic field is considered. Suppose that this flow admits an additional first integral F on N + 2 different energy levels which is polynomial in momenta of an arbitrary degree N with analytic periodic coefficients. It is proved that in this case the magnetic field and the metric are functions of one variable and there exists a linear in momenta first integral on all energy levels.",

keywords = "Magnetic geodesic flow, polynomial first integrals, QUASI-LINEAR SYSTEM, 1ST INTEGRALS, HAMILTONIAN-SYSTEMS, RIGIDITY, Magnetic geodesic flow, MECHANICAL SYSTEM, polynomial first integrals",

author = "Sergei Agapov and Alexandr Valyuzhenich",

year = "2019",

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doi = "10.3934/dcds.2019285",

language = "English",

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AU - Agapov, Sergei

AU - Valyuzhenich, Alexandr

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N2 - In this paper the geodesic flow on the 2-torus in a non-zero magnetic field is considered. Suppose that this flow admits an additional first integral F on N + 2 different energy levels which is polynomial in momenta of an arbitrary degree N with analytic periodic coefficients. It is proved that in this case the magnetic field and the metric are functions of one variable and there exists a linear in momenta first integral on all energy levels.

AB - In this paper the geodesic flow on the 2-torus in a non-zero magnetic field is considered. Suppose that this flow admits an additional first integral F on N + 2 different energy levels which is polynomial in momenta of an arbitrary degree N with analytic periodic coefficients. It is proved that in this case the magnetic field and the metric are functions of one variable and there exists a linear in momenta first integral on all energy levels.

KW - Magnetic geodesic flow, polynomial first integrals

KW - QUASI-LINEAR SYSTEM

KW - 1ST INTEGRALS

KW - HAMILTONIAN-SYSTEMS

KW - RIGIDITY

KW - Magnetic geodesic flow

KW - MECHANICAL SYSTEM

KW - polynomial first integrals

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JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

SN - 1078-0947

IS - 11

ER -

Polynomial integrals of magnetic geodesic flows on the 2-torus on several energy levels

Abstract

Keywords

OECD FOS+WOS

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