Academic Journal
Geodesics with unbounded speed on fluctuating surfaces
| العنوان: | Geodesics with unbounded speed on fluctuating surfaces |
|---|---|
| المؤلفون: | Clarke, Andrew Michael |
| المساهمون: | Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. UPCDS - Grup de Sistemes Dinàmics de la UPC |
| بيانات النشر: | Springer |
| سنة النشر: | 2024 |
| المجموعة: | Universitat Politècnica de Catalunya, BarcelonaTech: UPCommons - Global access to UPC knowledge |
| مصطلحات موضوعية: | Àrees temàtiques de la UPC::Matemàtiques i estadística, Hamiltonian systems, Hamiltonian dynamics, Geodesic flow, Non-autonomous perturbation, Arnold diffusion, Fermi acceleration, Sistemes hamiltonians, Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems |
| الوصف: | We construct C8 time-periodic fluctuating surfaces in R3 such that the corresponding non-autonomous geodesic flow has orbits along which the energy, and thus the speed goes to infinity. We begin with a static surface M in R3 on which the geodesic flow (with respect to the induced metric from R3) has a hyperbolic periodic orbit with a transverse homoclinic orbit. Taking this hyperbolic periodic orbit in an interval of energy levels gives us a normally hyperbolic invariant manifold ¿, the stable and unstable manifolds of which have a transverse homoclinic intersection. The surface M is embedded into R3 via a near-identity time-periodic embedding G : M ¿ R3. Then the pullback under G of the induced metric on G(M) is a time-periodic metric on M, and the corresponding geodesic flow has a normally hyperbolic invariant manifold close to ¿, with stable and unstable manifolds intersecting transversely along a homoclinic channel. Perturbative techniques are used to calculate the scattering map and construct pseudo-orbits that move up along the cylinder. The energy tends to infinity along such pseudo-orbits. Finally, existing shadowing methods are applied to establish the existence of actual orbits of the non-autonomous geodesic flow shadowing these pseudo-orbits. In the same way we prove the existence of oscillatory trajectories, along which the limit inferior of the energy is finite, but the limit superior is infinite. ; Peer Reviewed ; Postprint (published version) |
| نوع الوثيقة: | article in journal/newspaper |
| وصف الملف: | 16 p.; application/pdf |
| اللغة: | English |
| Relation: | https://link.springer.com/article/10.1134/S1560354724030018; http://hdl.handle.net/2117/415428 |
| DOI: | 10.1134/S1560354724030018 |
| الاتاحة: | http://hdl.handle.net/2117/415428 https://doi.org/10.1134/S1560354724030018 |
| Rights: | Attribution-NonCommercial-NoDerivatives 4.0 International ; http://creativecommons.org/licenses/by-nc-nd/4.0/ ; Restricted access - publisher's policy |
| رقم الانضمام: | edsbas.F8895A18 |
| قاعدة البيانات: | BASE |
| DOI: | 10.1134/S1560354724030018 |
|---|