Abstract:
We give a new proof of the existence of compact surfaces embedded in R3 with Anosov geodesic flows. This proof starts with a noncompact model surface whose geodesic flow is shown to be Anosov using a uniformly strictly invariant cone condition. Using a sequence of explicit maps based on the standard torus embedding, we produce compact embedded surfaces that can be seen as small perturbations of the Anosov model system and hence are themselves Anosov.
The first author was privileged to be a postdoctoral fellow with Professor Jürgen Moser at the ETH Zurich Switzerland in 1986-87 and greatly benefited from the lively intellectual atmosphere there. The second author was supported by a Summer Research Grant from Ithaca College.
Citation:
Victor Donnay, Daniel Visscher, “A New Proof of the Existence of Embedded Surfaces with Anosov Geodesic Flow”, Regul. Chaotic Dyn., 23:6 (2018), 685–694
\Bibitem{DonVis18}
\by Victor Donnay, Daniel Visscher
\paper A New Proof of the Existence of Embedded Surfaces with Anosov Geodesic Flow
\jour Regul. Chaotic Dyn.
\yr 2018
\vol 23
\issue 6
\pages 685--694
\mathnet{http://mi.mathnet.ru/rcd359}
\crossref{https://doi.org/10.1134/S1560354718060047}
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Linking options:
https://www.mathnet.ru/eng/rcd359
https://www.mathnet.ru/eng/rcd/v23/i6/p685
This publication is cited in the following 2 articles:
V. P. Kruglov, P. V. Kuptsov, “Theoretical Models of Physical Systems With Rough Chaos”, Izv. Vyss. Uchebn. Zaved.-Prikl. Nelineynaya Din., 29:1 (2021), 35–77
T. Fisher, B. Hasselblatt, “Hyperbolic flows”, Hyperbolic Flows, Zurich Lectures in Advanced Mathematics, European Mathematical Soc, 2019, 1–723
Citation in format AMSBIB
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