Global dynamics of the integrable Armbruster-Guckenheimer-Kim galactic potential

Jaume Llibre; Claudia Valls

doi:https://doi.org/10.1007/s10509-019-3624-y

Global dynamics of the integrable Armbruster-Guckenheimer-Kim galactic potential

Jaume Llibre, Claudia Valls

Department of Mathematics

Research output: Contribution to journal › Article › Research

3 Citations (Scopus)

Abstract

© 2019, Springer Nature B.V. We study the global dynamics of the completely integrable Armbruster-Guckenheimer-Kim galactic potential. In these cases this system has two first integrals H1 and H2 independent and in involution. Let Ih1 and Ih2 be the set of points of the phase space on which H1 and H2 take the values h1 and h2, respectively. The sets Ih1h2=Ih1∩Ih2 are invariant by the dynamics. We characterize the global flow on these sets and we describe the foliation of the phase space by the invariant sets Ih1h2.

Original language	English
Article number	130
Journal	Astrophysics and Space Science
Volume	364
DOIs	https://doi.org/10.1007/s10509-019-3624-y
Publication status	Published - 1 Aug 2019

Keywords

Armbruster-Guckenheimer-Kim galactic potential
Complete integrability
Invariant manifolds

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https://doi.org/10.1007/s10509-019-3624-y

https://ddd.uab.cat/record/221319

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AU - Valls, Claudia

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N2 - © 2019, Springer Nature B.V. We study the global dynamics of the completely integrable Armbruster-Guckenheimer-Kim galactic potential. In these cases this system has two first integrals H1 and H2 independent and in involution. Let Ih1 and Ih2 be the set of points of the phase space on which H1 and H2 take the values h1 and h2, respectively. The sets Ih1h2=Ih1∩Ih2 are invariant by the dynamics. We characterize the global flow on these sets and we describe the foliation of the phase space by the invariant sets Ih1h2.

AB - © 2019, Springer Nature B.V. We study the global dynamics of the completely integrable Armbruster-Guckenheimer-Kim galactic potential. In these cases this system has two first integrals H1 and H2 independent and in involution. Let Ih1 and Ih2 be the set of points of the phase space on which H1 and H2 take the values h1 and h2, respectively. The sets Ih1h2=Ih1∩Ih2 are invariant by the dynamics. We characterize the global flow on these sets and we describe the foliation of the phase space by the invariant sets Ih1h2.

KW - Armbruster-Guckenheimer-Kim galactic potential

KW - Complete integrability

KW - Invariant manifolds

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M3 - Article

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VL - 364

JO - Astrophysics and Space Science

JF - Astrophysics and Space Science

M1 - 130

ER -

Global dynamics of the integrable Armbruster-Guckenheimer-Kim galactic potential

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Keywords

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