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oai:www.repository.cam.ac.uk:1810/3900002025-12-19T20:50:09Zcom_1810_213747com_1810_256064col_1810_213748

Rigidity results for thermostats https://doi.org/10.17863/CAM.121703 Echevarría Cuesta, Javier 0000000292386101 Paternain, Gabriel A thermostat is a dynamical system modelling the motion of a particle on a surface under the influence of a force that is always orthogonal to its velocity. Since this force is allowed to depend on the particle's velocity, the system can be dissipative. As a generalization of geodesic and magnetic flows, thermostats provide a unified point of view to study many non-conservative dynamical systems, where the classical Hamiltonian structure is absent. We present rigidity results for thermostats that are Anosov, projectively Anosov, or have no conjugate points. For instance, we investigate rigidity under smooth orbit equivalences, and we explain how Eberlein's characterization of Anosov geodesic flows translates to thermostats. Our goal is to understand which results from the geodesic case extend to thermostats, despite the lack of volume preservation, while also highlighting the nuances that appear from greater dynamical complexity. To this end, we present examples and counterexamples illustrating the richer dynamics of thermostats. University of Cambridge 2025-05-10 Thesis Doctoral Doctor of Philosophy (PhD) eng Harding Distinguished Postgraduate Scholarship https://www.repository.cam.ac.uk/handle/1810/390000 https://www.repository.cam.ac.uk/bitstreams/ba50b25e-4e90-412a-915b-ceb7093a0721/download e6c115271477d1aeba6ecea12bc0b4e3 https://www.repository.cam.ac.uk/bitstreams/06fc121b-a12a-4b90-b7fa-c674de8eb1f8/download 87eda9de84448d1f82354d60eee3eb5f http://purl.org/NET/rdflicense/allrightsreserved mathematics chaotic dynamical systems geometry