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oai:recercat.cat:2117/4154282026-02-07T06:24:12Zcom_2072_1033col_2072_452950

Geodesics with unbounded speed on fluctuating surfaces Clarke, Andrew Michael Universitat Politècnica de Catalunya. Departament de Matemàtiques Universitat Politècnica de Catalunya. UPCDS - Grup de Sistemes Dinàmics de la UPC 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 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) 2024-05-29 Article Clarke, A. Geodesics with unbounded speed on fluctuating surfaces. "Regular and chaotic dynamics", 29 Maig 2024, vol. 29, p. 435-450. 1560-3547 https://hdl.handle.net/2117/415428 10.1134/S1560354724030018 eng https://link.springer.com/article/10.1134/S1560354724030018 http://creativecommons.org/licenses/by-nc-nd/4.0/ Restricted access - publisher's policy Attribution-NonCommercial-NoDerivatives 4.0 International 16 p. application/pdf Springer