Finsler metrics and action potentials
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- by Renato Iturriaga and Héctor Sánchez-Morgado PDF
- Proc. Amer. Math. Soc. 128 (2000), 3311-3316 Request permission
Abstract:
We study the behavior of Mañé’s action potential $\Phi _k$ associated to a convex superlinear Lagrangian, for $k$ bigger than the critical value $c(L)$. We obtain growth estimates for the action potential as a function of $k$. We also prove that the action potential can be written as $\Phi _k(x,y)=D_F(x,y)+f(y)-f(x)$ where $f$ is a smooth function and $D_F$ is the distance function associated to a Finsler metric.References
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Additional Information
- Renato Iturriaga
- Affiliation: CIMAT, A.P. 402, 36000, Guanajuato. Gto., México
- MR Author ID: 606377
- Email: renato@fractal.cimat.mx
- Héctor Sánchez-Morgado
- Affiliation: Instituto de Matemáticas, UNAM, Ciudad Universitaria, C. P. 04510, México, DF, México
- MR Author ID: 340702
- ORCID: 0000-0003-3981-408X
- Email: hector@matem.unam.mx
- Received by editor(s): December 28, 1998
- Published electronically: April 28, 2000
- Additional Notes: Both authors were partially supported by CONACYT-México grant # 28489-E
- Communicated by: Michael Handel
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 3311-3316
- MSC (2000): Primary 37J50, 70H30
- DOI: https://doi.org/10.1090/S0002-9939-00-05710-5
- MathSciNet review: 1777579