Investigating the Phase Space Dynamics of Hamiltonian Systems by the Origin-Fate Map
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arXiv
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| Format: | Preprint |
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2025
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| author | Moser, Ferris |
| author_facet | Moser, Ferris |
| contents | We investigate phase space transport in a two-dimensional stretched caldera potential using the Origin-Fate Map (OFM) framework, complemented by Lagrangian Descriptor (LD) analysis. The caldera potential, a model for reaction dynamics with multiple exit channels, is adjusted by a stretching factor lambda that controls the directional bias of the four-saddle landscape. Several OFMs are constructed for two Poincare surfaces of section using forwards and backwards symplectic integration to assign each initial condition a channel of origin and fate. Our results reproduce the highly symmetric lambda = 1.0 patterns reported in Hillebrand et al. (Phys. Rev. E 108, 024211, 2023), and reveal, for smaller lambda, pronounced channel imbalance, figure-eight transport loops, and complex mixed-channel chaotic regions. Long-time integrations show a reduction of trapped regions with boundaries that exhibit self-similarity under deep zoom, revealing fractal-like structures. High-resolution OFMs and LD gradient maps uncover lobe dynamics and manifold structures that govern transport, showing near-perfect alignment between LD ridges and OFM boundaries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13737 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Investigating the Phase Space Dynamics of Hamiltonian Systems by the Origin-Fate Map Moser, Ferris Chaotic Dynamics Dynamical Systems 37J05 (Primary), 37C29, 37D05, 37M05 (Secondary) We investigate phase space transport in a two-dimensional stretched caldera potential using the Origin-Fate Map (OFM) framework, complemented by Lagrangian Descriptor (LD) analysis. The caldera potential, a model for reaction dynamics with multiple exit channels, is adjusted by a stretching factor lambda that controls the directional bias of the four-saddle landscape. Several OFMs are constructed for two Poincare surfaces of section using forwards and backwards symplectic integration to assign each initial condition a channel of origin and fate. Our results reproduce the highly symmetric lambda = 1.0 patterns reported in Hillebrand et al. (Phys. Rev. E 108, 024211, 2023), and reveal, for smaller lambda, pronounced channel imbalance, figure-eight transport loops, and complex mixed-channel chaotic regions. Long-time integrations show a reduction of trapped regions with boundaries that exhibit self-similarity under deep zoom, revealing fractal-like structures. High-resolution OFMs and LD gradient maps uncover lobe dynamics and manifold structures that govern transport, showing near-perfect alignment between LD ridges and OFM boundaries. |
| title | Investigating the Phase Space Dynamics of Hamiltonian Systems by the Origin-Fate Map |
| topic | Chaotic Dynamics Dynamical Systems 37J05 (Primary), 37C29, 37D05, 37M05 (Secondary) |
| url | https://arxiv.org/abs/2511.13737 |