Hyperbolicity and exponential convergence of the Lax-Oleinik semigroup |
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Authors: | Renato Iturriaga Héctor Sánchez-Morgado |
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Institution: | a CIMAT, A.P. 402, 3600, Guanajuato, Gto, Mexico b Instituto de Matemáticas, Universidad Nacional Autónoma de México, México DF 04510, Mexico |
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Abstract: | For a convex superlinear Lagrangian on a compact manifold M it is known that there is a unique number c such that the Lax-Oleinik semigroup has a fixed point. Moreover for any u∈C(M,R) the uniform limit exists.In this paper we assume that the Aubry set consists in a finite number of periodic orbits or critical points and study the relation of the hyperbolicity of the Aubry set to the exponential rate of convergence of the Lax-Oleinik semigroup. |
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Keywords: | 37J50 49L25 70H20 |
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