On Periodic Orbits
نویسندگان
چکیده
منابع مشابه
On the Distribution of Periodic Orbits
Let f : M → M be a C-map on a smooth Riemannian manifold M and let Λ ⊂ M be a compact f -invariant locally maximal set. In this paper we obtain several results concerning the distribution of the periodic orbits of f |Λ. These results are non-invertible and, in particular, non-uniformly hyperbolic versions of well-known results by Bowen, Ruelle, and others in the case of hyperbolic diffeomorphis...
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These are supplemental lecture notes for the Undergraduate Summer School on Boundaries and Dynamics at Notre Dame University. They are incomplete. As of now, there is insufficient background for some of the topics, a complete absence of citations, some undefined objects, and several of the proofs could use greater details. Furthermore, these notes have not been vetted, so is a hope that student...
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Consider what is called the classical (Birkhoff) billiard problem: a particle moves in the planar convex domain D along the straight lines interacting with the boundary ∂D according to the Fermat’s law“ angle of reflection is equal to the angle of incidence”. In mathematical physics it is important to understand how many periodic orbits can be present in a planar billiard. Periodic orbits are t...
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ژورنال
عنوان ژورنال: Monthly Notices of the Royal Astronomical Society
سال: 1902
ISSN: 0035-8711,1365-2966
DOI: 10.1093/mnras/62.3.186