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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2603.19893 |
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| _version_ | 1866918413943701504 |
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| author | Guardia, Marcel Kaloshin, Vadim Martín, Pau Roldan, Pablo |
| author_facet | Guardia, Marcel Kaloshin, Vadim Martín, Pau Roldan, Pablo |
| contents | In this paper we discuss the existence of a normally hyperbolic invariant lamination (NHIL) at the Kirkwood gap $3:1$ for the Restricted Planar Elliptic 3 Body Problem. This problem models the Sun-Jupiter-Asteroid dynamics. We also show that the induced dynamics on the NHIL is a partially hyperbolic skew-shift which is of the form \[ f:(ω,I,θ)\to (σω, I+e_0 A_ω(I)\cos(θ+ψ_ω)+\mathcal{O}(e^2_0), θ+Ω_ω(I)+\mathcal{O}(e_0)),\] where $I\in [a,b], θ\in \mathbb T, ω\inΣ=\{0,1\}^\mathbb Z$, the space of sequences of $0,1$'s, $σ:Σ\to Σ$ is the shift in this space, $Ω_ω$ is the shear, $A_ω$ is an amplitude, and $e_0$ is the eccentricity of Jupiter, which is taken as a small parameter.
In the companion paper arXiv:2603.19894, relying on these skew-shift, we show the existence of stochastic diffusing behavior for Asteroids belonging to the Kirkwood gap provided the eccentricity of Jupiter is $e_0$ small enough.
Key ingredients to construct the NHIL are the separatrix map associated to homoclinic channels to a normally hyperbolic invariant cylinder and an isolating block construction. Some of the necessary non-degeneracy conditions are verified numerically. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_19893 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Computation of a separatrix map and a normally hyperbolic invariant lamination for the RP3BP Guardia, Marcel Kaloshin, Vadim Martín, Pau Roldan, Pablo Dynamical Systems 37D05 (Primary), 37N05 (Secondary) In this paper we discuss the existence of a normally hyperbolic invariant lamination (NHIL) at the Kirkwood gap $3:1$ for the Restricted Planar Elliptic 3 Body Problem. This problem models the Sun-Jupiter-Asteroid dynamics. We also show that the induced dynamics on the NHIL is a partially hyperbolic skew-shift which is of the form \[ f:(ω,I,θ)\to (σω, I+e_0 A_ω(I)\cos(θ+ψ_ω)+\mathcal{O}(e^2_0), θ+Ω_ω(I)+\mathcal{O}(e_0)),\] where $I\in [a,b], θ\in \mathbb T, ω\inΣ=\{0,1\}^\mathbb Z$, the space of sequences of $0,1$'s, $σ:Σ\to Σ$ is the shift in this space, $Ω_ω$ is the shear, $A_ω$ is an amplitude, and $e_0$ is the eccentricity of Jupiter, which is taken as a small parameter. In the companion paper arXiv:2603.19894, relying on these skew-shift, we show the existence of stochastic diffusing behavior for Asteroids belonging to the Kirkwood gap provided the eccentricity of Jupiter is $e_0$ small enough. Key ingredients to construct the NHIL are the separatrix map associated to homoclinic channels to a normally hyperbolic invariant cylinder and an isolating block construction. Some of the necessary non-degeneracy conditions are verified numerically. |
| title | Computation of a separatrix map and a normally hyperbolic invariant lamination for the RP3BP |
| topic | Dynamical Systems 37D05 (Primary), 37N05 (Secondary) |
| url | https://arxiv.org/abs/2603.19893 |