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The Multiplicity Problem for Periodic Orbits of Magnetic Flows on the 2-Sphere. / Abbondandolo, Alberto; Asselle, Luca; Benedetti, Gabriele et al.

In: Advanced Nonlinear Studies, Vol. 17, No. 1, 02.01.2017, p. 17-30.

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

Harvard

Abbondandolo, A, Asselle, L, Benedetti, G, Mazzucchelli, M & Taimanov, IA 2017, 'The Multiplicity Problem for Periodic Orbits of Magnetic Flows on the 2-Sphere', Advanced Nonlinear Studies, vol. 17, no. 1, pp. 17-30. https://doi.org/10.1515/ans-2016-6003

APA

Abbondandolo, A., Asselle, L., Benedetti, G., Mazzucchelli, M., & Taimanov, I. A. (2017). The Multiplicity Problem for Periodic Orbits of Magnetic Flows on the 2-Sphere. Advanced Nonlinear Studies, 17(1), 17-30. https://doi.org/10.1515/ans-2016-6003

Vancouver

Abbondandolo A, Asselle L, Benedetti G, Mazzucchelli M, Taimanov IA. The Multiplicity Problem for Periodic Orbits of Magnetic Flows on the 2-Sphere. Advanced Nonlinear Studies. 2017 Jan 2;17(1):17-30. doi: 10.1515/ans-2016-6003

Author

Abbondandolo, Alberto ; Asselle, Luca ; Benedetti, Gabriele et al. / The Multiplicity Problem for Periodic Orbits of Magnetic Flows on the 2-Sphere. In: Advanced Nonlinear Studies. 2017 ; Vol. 17, No. 1. pp. 17-30.

BibTeX

@article{84c603adaa70497db37cde89698d82a3,
title = "The Multiplicity Problem for Periodic Orbits of Magnetic Flows on the 2-Sphere",
abstract = "We consider magnetic Tonelli Hamiltonian systems on the cotangent bundle of the 2-sphere, where the magnetic form is not necessarily exact. It is known that, on very low and on high energy levels, these systems may have only finitely many periodic orbits. Our main result asserts that almost all energy levels in a precisely characterized intermediate range (e(0), e(1)) possess infinitely many periodic orbits. Such a range of energies is non-empty, for instance, in the physically relevant case where the Tonelli Lagrangian is a kinetic energy and the magnetic form is oscillating (in which case, e(0) = 0 is the minimal energy of the system).",
keywords = "Tonelli Lagrangians, Magnetic Flows, Hamiltonian Systems, Periodic Orbits, Mane Critical Values, LAGRANGIAN SYSTEMS, GEODESICS, SURFACES, FIELDS, Ma{\~n}{\'e} Critical Values",
author = "Alberto Abbondandolo and Luca Asselle and Gabriele Benedetti and Marco Mazzucchelli and Taimanov, {Iskander A.}",
year = "2017",
month = jan,
day = "2",
doi = "10.1515/ans-2016-6003",
language = "English",
volume = "17",
pages = "17--30",
journal = "Advanced Nonlinear Studies",
issn = "1536-1365",
publisher = "Walter de Gruyter GmbH",
number = "1",

}

RIS

TY - JOUR

T1 - The Multiplicity Problem for Periodic Orbits of Magnetic Flows on the 2-Sphere

AU - Abbondandolo, Alberto

AU - Asselle, Luca

AU - Benedetti, Gabriele

AU - Mazzucchelli, Marco

AU - Taimanov, Iskander A.

PY - 2017/1/2

Y1 - 2017/1/2

N2 - We consider magnetic Tonelli Hamiltonian systems on the cotangent bundle of the 2-sphere, where the magnetic form is not necessarily exact. It is known that, on very low and on high energy levels, these systems may have only finitely many periodic orbits. Our main result asserts that almost all energy levels in a precisely characterized intermediate range (e(0), e(1)) possess infinitely many periodic orbits. Such a range of energies is non-empty, for instance, in the physically relevant case where the Tonelli Lagrangian is a kinetic energy and the magnetic form is oscillating (in which case, e(0) = 0 is the minimal energy of the system).

AB - We consider magnetic Tonelli Hamiltonian systems on the cotangent bundle of the 2-sphere, where the magnetic form is not necessarily exact. It is known that, on very low and on high energy levels, these systems may have only finitely many periodic orbits. Our main result asserts that almost all energy levels in a precisely characterized intermediate range (e(0), e(1)) possess infinitely many periodic orbits. Such a range of energies is non-empty, for instance, in the physically relevant case where the Tonelli Lagrangian is a kinetic energy and the magnetic form is oscillating (in which case, e(0) = 0 is the minimal energy of the system).

KW - Tonelli Lagrangians

KW - Magnetic Flows

KW - Hamiltonian Systems

KW - Periodic Orbits

KW - Mane Critical Values

KW - LAGRANGIAN SYSTEMS

KW - GEODESICS

KW - SURFACES

KW - FIELDS

KW - Mañé Critical Values

UR - http://www.scopus.com/inward/record.url?scp=85011634303&partnerID=8YFLogxK

U2 - 10.1515/ans-2016-6003

DO - 10.1515/ans-2016-6003

M3 - Article

VL - 17

SP - 17

EP - 30

JO - Advanced Nonlinear Studies

JF - Advanced Nonlinear Studies

SN - 1536-1365

IS - 1

ER -

ID: 18736082