Continuation and stability deduction of resonant periodic orbits in three dimensional systems

Kyriaki I. Antoniadou, George Voyatzis, Harry Varvoglis

Research output: Contribution to conferencePaper

Abstract

In dynamical systems of few degrees of freedom, periodic solutions consist the backbone of the phase space and the determination and computation of their stability is crucial for understanding the global dynamics. In this paper we study the classical three body problem in three dimensions and use its dynamics to assess the long-term evolution of extrasolar systems. We compute periodic orbits, which correspond to exact resonant motion, and determine their linear stability. By computing maps of dynamical stability we show that stable periodic orbits are surrounded in phase space with regular motion even in systems with more than two degrees of freedom, while chaos is apparent close to unstable ones. Therefore, families of stable periodic orbits, indeed, consist backbones of the stability domains in phase space.
Original languageEnglish
Publication statusPublished - 2014

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deduction
orbits
degrees of freedom
three body problem
dynamical systems
chaos

Keywords

  • Astrophysics - Earth and Planetary Astrophysics
  • Nonlinear Sciences - Chaotic Dynamics

Cite this

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title = "Continuation and stability deduction of resonant periodic orbits in three dimensional systems",
abstract = "In dynamical systems of few degrees of freedom, periodic solutions consist the backbone of the phase space and the determination and computation of their stability is crucial for understanding the global dynamics. In this paper we study the classical three body problem in three dimensions and use its dynamics to assess the long-term evolution of extrasolar systems. We compute periodic orbits, which correspond to exact resonant motion, and determine their linear stability. By computing maps of dynamical stability we show that stable periodic orbits are surrounded in phase space with regular motion even in systems with more than two degrees of freedom, while chaos is apparent close to unstable ones. Therefore, families of stable periodic orbits, indeed, consist backbones of the stability domains in phase space.",
keywords = "Astrophysics - Earth and Planetary Astrophysics, Nonlinear Sciences - Chaotic Dynamics",
author = "Antoniadou, {Kyriaki I.} and George Voyatzis and Harry Varvoglis",
year = "2014",
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Continuation and stability deduction of resonant periodic orbits in three dimensional systems. / Antoniadou, Kyriaki I.; Voyatzis, George; Varvoglis, Harry.

2014.

Research output: Contribution to conferencePaper

TY - CONF

T1 - Continuation and stability deduction of resonant periodic orbits in three dimensional systems

AU - Antoniadou, Kyriaki I.

AU - Voyatzis, George

AU - Varvoglis, Harry

PY - 2014

Y1 - 2014

N2 - In dynamical systems of few degrees of freedom, periodic solutions consist the backbone of the phase space and the determination and computation of their stability is crucial for understanding the global dynamics. In this paper we study the classical three body problem in three dimensions and use its dynamics to assess the long-term evolution of extrasolar systems. We compute periodic orbits, which correspond to exact resonant motion, and determine their linear stability. By computing maps of dynamical stability we show that stable periodic orbits are surrounded in phase space with regular motion even in systems with more than two degrees of freedom, while chaos is apparent close to unstable ones. Therefore, families of stable periodic orbits, indeed, consist backbones of the stability domains in phase space.

AB - In dynamical systems of few degrees of freedom, periodic solutions consist the backbone of the phase space and the determination and computation of their stability is crucial for understanding the global dynamics. In this paper we study the classical three body problem in three dimensions and use its dynamics to assess the long-term evolution of extrasolar systems. We compute periodic orbits, which correspond to exact resonant motion, and determine their linear stability. By computing maps of dynamical stability we show that stable periodic orbits are surrounded in phase space with regular motion even in systems with more than two degrees of freedom, while chaos is apparent close to unstable ones. Therefore, families of stable periodic orbits, indeed, consist backbones of the stability domains in phase space.

KW - Astrophysics - Earth and Planetary Astrophysics

KW - Nonlinear Sciences - Chaotic Dynamics

M3 - Paper

ER -