scholarly journals Aubry-Mather theory for functions on lattices

1997 ◽  
Vol 3 (1) ◽  
pp. 135-151 ◽  
Author(s):  
Hans Koch ◽  
◽  
Rafael De La Llave ◽  
Charles Radin ◽  
Keyword(s):  
Mather Theory

scholarly journals Inequalities and the Aubry-Mather theory of Hamilton-Jacobi equations

2009 ◽  
Vol 8 (2) ◽  
pp. 683-688
Author(s):  
Yasuhiro Fujita ◽  
◽  
Katsushi Ohmori ◽  
Keyword(s):  
Mather Theory ◽  
Jacobi Equations

Construction of invariant measures supported within the gaps of Aubry–Mather sets

1996 ◽  
Vol 16 (1) ◽  
pp. 51-86 ◽  
Author(s):  
Giovanni Forni
Keyword(s):  
Variational Approach ◽  
Invariant Measures ◽  
Positive Entropy ◽  
Almost Periodic ◽  
Invariant Curves ◽  
Mather Theory ◽  
Entropy Measures ◽  
Twist Maps ◽  
Minimization Procedure ◽  
Area Preserving

AbstractThis paper represents a contribution to the variational approach to the understanding of the dynamics of exact area-preserving monotone twist maps of the annulus, currently known as the Aubry–Mather theory. The method introduced by Mather to construct invariant measures of Denjoy type is extended to produce almost-periodic measures, having arbitrary rationally independent frequencies, and positive entropy measures, supported within the gaps of Aubry–Mather sets which do not lie on invariant curves. This extension is based on a generalized version of the Percival's Lagrangian and on a new minimization procedure, which also gives a simplified proof of the basic existence theorem for the Aubry–Mather sets.

scholarly journals Optimal results in Lorentzian Aubry–Mather theory

2020 ◽  
Author(s):  
Stefan Suhr
Keyword(s):  
Fixed Point ◽  
Invariant Measures ◽  
Lipschitz Continuity ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Multiplicity Results ◽  
Time Separation ◽  
Abelian Cover ◽  
Mather Theory ◽  
Maximal Invariant

AbstractThis article complements the Lorentzian Aubry–Mather Theory in Suhr (Geom Dedicata 160:91–117, 2012; J Fixed Point Theory Appl 21:71, 2019) by giving optimal multiplicity results for the number of maximal invariant measures. As an application the optimal Lipschitz continuity of the time separation on the Abelian cover is established.

scholarly journals Ghost circles in lattice Aubry–Mather theory

2012 ◽  
Vol 252 (4) ◽  
pp. 3163-3208 ◽  
Author(s):  
Blaz Mramor ◽  
Bob Rink
Keyword(s):  
Mather Theory

scholarly journals Percival Lagrangian approach to the Aubry–Mather theory

2012 ◽  
Vol 30 (2) ◽  
pp. 182-208 ◽  
Author(s):  
Xifeng Su ◽  
Rafael de la Llave
Keyword(s):  
Lagrangian Approach ◽  
Mather Theory

scholarly journals Randomly perturbed dynamical systems and Aubry-Mather theory

2009 ◽  
Vol 2 (3/4) ◽  
pp. 139 ◽  
Author(s):  
Fabio Camilli ◽  
Annalisa Cesaroni ◽  
Antonio Siconolfi
Keyword(s):  
Dynamical Systems ◽  
Mather Theory
Sign in / Sign up

Export Citation Format

Share Document