THE SYMMETRIC HORSESHOE PERIODIC FAMILIES AND THE LYAPUNOV PLANAR FAMILY AROUND<i>L</i><sub>3</sub>

Hou, Xiyun; Liu, L.

doi:10.1088/0004-6256/136/1/67

Cited by 12 publications

(3 citation statements)

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“…Studying the invariant manifold structures for the collinear libration points is fundamental for understanding the capture and resonance transition of various comets (see Koon et al 2000). An extensive literature on the periodic orbits around the libration points and their stability exists for this problem (see, for example, Bruno & Varin 2007;Hou & Liu 2008;Barrabés, Mondelo & Ollé 2009). …”

Section: Application To the Sun-jupiter Problemmentioning

confidence: 99%

Comparison of chaos detection methods in the circular restricted three‐body problem

Racoveanu

2014

Astron Nachr

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In this study, a sample of orbits is considered in the framework of the planar circular restricted three-body problem. In order to separate ordered from chaotic orbits three numerical methods are compared: the Largest Lyapunov Characteristic Exponent (LLCE) and the Smaller Alignment Index (SALI) provide a fairly good characterization of the chaotic motions, while the computational time required is of the same order; the Correlation Dimension (CD) has the advantage of correctly classifying sticky orbits, but at the expense of a longer computational time. In order to classify a given orbit, any pair of the three methods can be considered, but LLCE and SALI are recommended due to their speed.

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Section: Application To the Sun-jupiter Problemmentioning

confidence: 99%

Comparison of chaos detection methods in the circular restricted three‐body problem

Racoveanu

2014

Astron Nachr

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“…The homo family here is not a unique phenomenon in the Circular Restricted Three-Body Problem. For example, many symmetric horseshoe periodic families are also homo families which terminate onto themselves (Hou & Liu 2008c).…”

Section: Homo Familymentioning

confidence: 99%

On critical values concerning the evolution of the long period families

Hou¹

2009

Res. Astron. Astrophys.

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In a previous paper, we proposed another special critical value concerning the evolution of the long period family around the equilateral equilibrium points, besides the two values given by Henrard. Are there any other special critical values? After studying the stability curves of the long period family carefully, we gave a negative answer. During the study, we found an interesting family of periodic orbits which we called the homo family. We studied the evolution of this family following the increase of µ. With these findings, we were able to explain the origin of the four branches of periodic families emanating from L 4 and the stability results of the equilateral equilibrium points.

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“…1 Except Mercury, Venus, and Saturn, this kind of small bodies have been found for all the other five planets in our solar system (Emery et al 2015). Most of the time, these objects follow tadpole orbits around one TLP, but there are a few outlaws that may "jump" between the two TLPs (Tsiganis et al 2000;Connors et al 2011;Schwarz and Dvorak 2012) following a horseshoe-like orbit (Hou and Liu 2008;Oshima and Yanao 2015). Except the Solar System, this kind of objects in the exoplanetary systems recently also begin to draw researchers' interest (Haghighipour et al 2013;Isabel Páez and Efthymiopoulos 2015).…”

Section: Introductionmentioning

confidence: 99%

Dynamics of the Jupiter Trojans with Saturn’s perturbation when the two planets are in migration

Hou

Scheeres

Liu

2016

Celest Mech Dyn Astr

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In a previous paper (Hou et al. in Celest Mech Dyn Astron 119:119-142, 2014a), the problem of dynamical symmetry between two Jupiter triangular libration points (TLPs) with Saturn's perturbation in the present configuration of the two planets was studied. A small short-time scale spatial asymmetry exists but gradually disappears with the time going, so the planar stable regions around the two Jupiter TLPs should be dynamically symmetric from a longtime perspective. In this paper, the symmetry problem is studied when the two planets are in migration. Several mechanisms that can cause asymmetries are discussed. Studies show that three important ones are the large short-time scale spatial asymmetry when Jupiter and Saturn are in resonance, the changing orbits of Jupiter and Saturn in the planet migration process, and the chaotic nature of Trojan orbits during the planet migration process. Their joint effects can cause an observable difference to the two Jupiter Trojan swarms. The thermal Yarkovsky effect is also found to be able to cause dynamical differences to the two TLPs, but generally they are too small to be practically observed.

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THE SYMMETRIC HORSESHOE PERIODIC FAMILIES AND THE LYAPUNOV PLANAR FAMILY AROUNDL₃

Cited by 12 publications

References 10 publications

Comparison of chaos detection methods in the circular restricted three‐body problem

Comparison of chaos detection methods in the circular restricted three‐body problem

On critical values concerning the evolution of the long period families

Dynamics of the Jupiter Trojans with Saturn’s perturbation when the two planets are in migration

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THE SYMMETRIC HORSESHOE PERIODIC FAMILIES AND THE LYAPUNOV PLANAR FAMILY AROUNDL3

Cited by 12 publications

References 10 publications

Comparison of chaos detection methods in the circular restricted three‐body problem

Comparison of chaos detection methods in the circular restricted three‐body problem

On critical values concerning the evolution of the long period families

Dynamics of the Jupiter Trojans with Saturn’s perturbation when the two planets are in migration

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Product

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THE SYMMETRIC HORSESHOE PERIODIC FAMILIES AND THE LYAPUNOV PLANAR FAMILY AROUNDL₃