Chaotic phenomena in generic unfoldings of the Hamilton Hopf bifurcation with emphasis on the restricted planar circular 3-body problem beyond the Gascheau-Routh mass ratio
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908636077359104 |
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| author | Baldomá, Inmaculada Martín, Pau Scarcella, Donato |
| author_facet | Baldomá, Inmaculada Martín, Pau Scarcella, Donato |
| contents | In this work, we prove that a generic unfolding of an analytic Hamiltonian Hopf singularity (in an open set with codimension 1 boundary) possesses transverse homoclinic orbits for subcritical values of the parameter close to the bifurcation parameter. As a consequence, these systems display chaotic dynamics with arbitrarily large topological entropy. We verify that the Hamiltonian of the restricted planar circular three-body problem (RPC3BP) close to the Lagrangian point $L_4$ falls within this open set. The generic condition ensuring the presence of transversal homoclinic intersections is subtle and involves the so-called Stokes constant. Thus, in the case of the RPC3BP close to $L_4$, our result holds conditionally on the value of this constant. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_05333 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chaotic phenomena in generic unfoldings of the Hamilton Hopf bifurcation with emphasis on the restricted planar circular 3-body problem beyond the Gascheau-Routh mass ratio Baldomá, Inmaculada Martín, Pau Scarcella, Donato Dynamical Systems In this work, we prove that a generic unfolding of an analytic Hamiltonian Hopf singularity (in an open set with codimension 1 boundary) possesses transverse homoclinic orbits for subcritical values of the parameter close to the bifurcation parameter. As a consequence, these systems display chaotic dynamics with arbitrarily large topological entropy. We verify that the Hamiltonian of the restricted planar circular three-body problem (RPC3BP) close to the Lagrangian point $L_4$ falls within this open set. The generic condition ensuring the presence of transversal homoclinic intersections is subtle and involves the so-called Stokes constant. Thus, in the case of the RPC3BP close to $L_4$, our result holds conditionally on the value of this constant. |
| title | Chaotic phenomena in generic unfoldings of the Hamilton Hopf bifurcation with emphasis on the restricted planar circular 3-body problem beyond the Gascheau-Routh mass ratio |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2511.05333 |