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

Standard

Polynomial integrals of magnetic geodesic flows on the 2-torus on several energy levels. / Agapov, Sergei; Valyuzhenich, Alexandr.

In: Discrete and Continuous Dynamical Systems- Series A, Vol. 39, No. 11, 11.2019, p. 6565-6583.

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

Harvard

Agapov, S & Valyuzhenich, A 2019, 'Polynomial integrals of magnetic geodesic flows on the 2-torus on several energy levels', Discrete and Continuous Dynamical Systems- Series A, vol. 39, no. 11, pp. 6565-6583. https://doi.org/10.3934/dcds.2019285

APA

Agapov, S., & Valyuzhenich, A. (2019). Polynomial integrals of magnetic geodesic flows on the 2-torus on several energy levels. Discrete and Continuous Dynamical Systems- Series A, 39(11), 6565-6583. https://doi.org/10.3934/dcds.2019285

Vancouver

Agapov S, Valyuzhenich A. Polynomial integrals of magnetic geodesic flows on the 2-torus on several energy levels. Discrete and Continuous Dynamical Systems- Series A. 2019 Nov;39(11):6565-6583. doi: 10.3934/dcds.2019285

Author

Agapov, Sergei ; Valyuzhenich, Alexandr. / Polynomial integrals of magnetic geodesic flows on the 2-torus on several energy levels. In: Discrete and Continuous Dynamical Systems- Series A. 2019 ; Vol. 39, No. 11. pp. 6565-6583.

BibTeX

@article{dc61d68fc349470bac6d21ca935b4912,

title = "Polynomial integrals of magnetic geodesic flows on the 2-torus on several energy levels",

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",

month = nov,

doi = "10.3934/dcds.2019285",

language = "English",

volume = "39",

pages = "6565--6583",

journal = "Discrete and Continuous Dynamical Systems- Series A",

issn = "1078-0947",

publisher = "American Institute of Mathematical Sciences",

number = "11",

}

RIS

TY - JOUR

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

AU - Agapov, Sergei

AU - Valyuzhenich, Alexandr

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 -

ID: 21347978