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2026
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| Online Access: | https://doi.org/10.5281/zenodo.19583276 |
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| _version_ | 1866901987855958016 |
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| author | Doucette, Doug |
| author_facet | Doucette, Doug |
| contents | <p class="MsoNormal"><span>A longstanding paradox in nonlinear Hamiltonian dynamics is that chaos does not reliably imply rapid transport, rapid mixing, or prompt loss of coherence. A system may possess chaotic layers, resonance structure, and formal routes to instability while nevertheless remaining effectively confined for extraordinarily long times. Trajectories may become trapped near regular islands, cantori, or resonance layers; transport may become intermittent and heavy-tailed; and instability that exists in principle may remain dynamically irrelevant in practice. This paper presents a mathematical reformulation of the partial resolution proposed in Doucette (2026). The central claim is that when a system belongs to the Trojan Universality Class—that is, when its local dynamics reduce to a two-mode, spectrally separated, nearly integrable Hamiltonian skeleton—chaos is not abolished but throttled. We formulate the relevant hypotheses, restate the principal structural results in theorem form, and explain their dynamical meaning. The resulting picture is that spectral separation suppresses low-order resonance, finite-order Birkhoff normal forms restore truncated integrability, KAM/Nekhoroshev mechanisms enforce long confinement, mixed phase space yields heavy-tail transport rather than ordinary diffusion, and loss of Trojan protection occurs only through a small number of structurally identifiable exit routes. The resolution is partial because it applies only to systems satisfying Trojan admission conditions and does not, by itself, provide universal quantitative diffusion rates for arbitrary chaotic Hamiltonian systems.</span></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19583276 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Chaotic Persistence and The Paradox of Sticky Chaos Doucette, Doug <p class="MsoNormal"><span>A longstanding paradox in nonlinear Hamiltonian dynamics is that chaos does not reliably imply rapid transport, rapid mixing, or prompt loss of coherence. A system may possess chaotic layers, resonance structure, and formal routes to instability while nevertheless remaining effectively confined for extraordinarily long times. Trajectories may become trapped near regular islands, cantori, or resonance layers; transport may become intermittent and heavy-tailed; and instability that exists in principle may remain dynamically irrelevant in practice. This paper presents a mathematical reformulation of the partial resolution proposed in Doucette (2026). The central claim is that when a system belongs to the Trojan Universality Class—that is, when its local dynamics reduce to a two-mode, spectrally separated, nearly integrable Hamiltonian skeleton—chaos is not abolished but throttled. We formulate the relevant hypotheses, restate the principal structural results in theorem form, and explain their dynamical meaning. The resulting picture is that spectral separation suppresses low-order resonance, finite-order Birkhoff normal forms restore truncated integrability, KAM/Nekhoroshev mechanisms enforce long confinement, mixed phase space yields heavy-tail transport rather than ordinary diffusion, and loss of Trojan protection occurs only through a small number of structurally identifiable exit routes. The resolution is partial because it applies only to systems satisfying Trojan admission conditions and does not, by itself, provide universal quantitative diffusion rates for arbitrary chaotic Hamiltonian systems.</span></p> |
| title | Chaotic Persistence and The Paradox of Sticky Chaos |
| url | https://doi.org/10.5281/zenodo.19583276 |