Bi-invariant metrics for symplectic twist mappings on 𝑏𝑜𝑙𝑑𝑠𝑦𝑚𝑏𝑜𝑙𝑇*𝕋ⁿ and an application in Aubry-Mather theory

1998 ◽  
pp. 137-148 ◽  
Author(s):  
Karl Siburg
Keyword(s):  
Invariant Metrics ◽  
Mather Theory ◽  
Twist Mappings

scholarly journals Estimates for invariant metrics on $\mathbb C$-convex domains

2011 ◽  
Vol 363 (12) ◽  
pp. 6245-6256 ◽  
Author(s):  
Nikolai Nikolov ◽  
Peter Pflug ◽  
Włodzimierz Zwonek
Keyword(s):  
Invariant Metrics ◽  
Convex Domains

Geometric structures on manifolds and holonomy-invariant metrics

1997 ◽  
Vol 9 (9) ◽  
Author(s):  
Suhyoung Choi ◽  
Hyunkoo Lee
Keyword(s):  
Invariant Metrics ◽  
Geometric Structures

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

scholarly journals Stability for the vertical rotation interval of twist mappings

2006 ◽  
Vol 14 (4) ◽  
pp. 631-642
Author(s):  
Salvador Addas-Zanata ◽  
Keyword(s):  
Rotation Interval ◽  
Twist Mappings

scholarly journals Scale Invariant Metrics of Volumetric Datasets

2015 ◽  
Vol 8 (1) ◽  
pp. 403-425 ◽  
Author(s):  
Dan Raviv ◽  
Ramesh Raskar
Keyword(s):  
Invariant Metrics ◽  
Scale Invariant

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.

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