We investigate the heteroclinic connections between the stable and unstable manifolds of the unstable periodic orbits associated with the most important mean-motion resonances (MMRs) in the Sun–Jupiter planar restricted three-body problem. In particular, we explicitly compute the stable and unstable manifolds of the unstable periodic orbits associated with the first-order interior MMRs 2:1, 3:2, and the exterior MMR 2:3. Furthermore, we compute short-time fast Lyapunov indicator (FLI) maps showing the chaotic saddle structure created by the stable and unstable manifolds of several interior or exterior MMRs other than the 1:1 (co-orbital) resonance. Transits of particles from the exterior to the interior of the orbit of Jupiter and vice versa are allowed for values of the Jacobi energy mapped to Tisserand parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$T<3.0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>T</mi> <mo><</mo> <mn>3.0</mn> </mrow> </math></EquationSource> </InlineEquation>. Such transits are shown to exist through a variety of heteroclinic channels. Besides the classical ones established in Koon et al. (<CitationRef CitationID="CR32">2000</CitationRef>, <CitationRef CitationID="CR33">2001</CitationRef>); Barrabés et al. (<CitationRef CitationID="CR2">2009</CitationRef>, <CitationRef CitationID="CR3">2013</CitationRef>), we give evidence of heteroclinic connections between the manifolds of the short-period orbits around L3 and of the periodic orbits associated with interior or exterior first-order MMRs. Moreover, we observe direct heteroclinic connections between the manifolds of the interior with exterior MMRs, which do not involve the manifolds of any of the periodic orbits of the co-orbital resonance. Through the manifolds of the MMRs and the corresponding ‘ridges’ in the numerical FLI maps, we explain the ‘arches-of-chaos’ structures (Todorovic et al. <CitationRef CitationID="CR55">2020</CitationRef>) found in FLI maps in the asteroid plane of orbital elements (a, e). The chaotic orbits shadowing the heteroclinic orbits exhibit ‘resonance hopping’, indicating a possible connection to the behavior reported in the literature as regards the orbits of several real Solar System objects classified as quasi-Hildas (QH) or Jupiter-family comets (JFC). Most of our results are obtained in the framework of the planar circular RTBP. However, through FLI maps we show that the manifold connections observed in the circular problem persist in the elliptic problem as well.

Arches of chaos, heteroclinic connections of first-order MMRs, and the chaotic transport of small bodies in the Sun–Jupiter system

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发表日期：

2026年6月26日

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Alessia Francesca Guido,
Christos Efthymiopoulos

摘要

We investigate the heteroclinic connections between the stable and unstable manifolds of the unstable periodic orbits associated with the most important mean-motion resonances (MMRs) in the Sun–Jupiter planar restricted three-body problem. In particular, we explicitly compute the stable and unstable manifolds of the unstable periodic orbits associated with the first-order interior MMRs 2:1, 3:2, and the exterior MMR 2:3. Furthermore, we compute short-time fast Lyapunov indicator (FLI) maps showing the chaotic saddle structure created by the stable and unstable manifolds of several interior or exterior MMRs other than the 1:1 (co-orbital) resonance. Transits of particles from the exterior to the interior of the orbit of Jupiter and vice versa are allowed for values of the Jacobi energy mapped to Tisserand parameter $T<3.0$ $T < 3.0$ . Such transits are shown to exist through a variety of heteroclinic channels. Besides the classical ones established in Koon et al. (2000, 2001); Barrabés et al. (2009, 2013), we give evidence of heteroclinic connections between the manifolds of the short-period orbits around L3 and of the periodic orbits associated with interior or exterior first-order MMRs. Moreover, we observe direct heteroclinic connections between the manifolds of the interior with exterior MMRs, which do not involve the manifolds of any of the periodic orbits of the co-orbital resonance. Through the manifolds of the MMRs and the corresponding ‘ridges’ in the numerical FLI maps, we explain the ‘arches-of-chaos’ structures (Todorovic et al. 2020) found in FLI maps in the asteroid plane of orbital elements (a, e). The chaotic orbits shadowing the heteroclinic orbits exhibit ‘resonance hopping’, indicating a possible connection to the behavior reported in the literature as regards the orbits of several real Solar System objects classified as quasi-Hildas (QH) or Jupiter-family comets (JFC). Most of our results are obtained in the framework of the planar circular RTBP. However, through FLI maps we show that the manifold connections observed in the circular problem persist in the elliptic problem as well.