TY - JOUR

T1 - Polynomial integrals of magnetic geodesic flows on the 2-torus on several energy levels

AU - Agapov, Sergei

AU - Valyuzhenich, Alexandr

N1 - Publisher Copyright: © 2019 American Institute of Mathematical Sciences. All rights reserved.

PY - 2019/11

Y1 - 2019/11

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

UR - http://www.scopus.com/inward/record.url?scp=85071244586&partnerID=8YFLogxK

U2 - 10.3934/dcds.2019285

DO - 10.3934/dcds.2019285

M3 - Article

AN - SCOPUS:85071244586

VL - 39

SP - 6565

EP - 6583

JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

SN - 1078-0947

IS - 11

ER -