Jump to ContentJump to Main Navigation

You are looking at 1-5 of 5 items

  • Keywords: Aubry set x
Clear All Modify Search

View:

Action-Minimizing Curves for Tonelli Lagrangians

Alfonso Sorrentino

in Action-minimizing Methods in Hamiltonian Dynamics (MN-50): An Introduction to Aubry-Mather Theory

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691164502
eISBN:
9781400866618
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691164502.003.0004
Subject:
Mathematics, Applied Mathematics

This chapter discusses the notion of action-minimizing orbits. In particular, it defines the other two families of invariant sets, the so-called Aubry and Mañé sets. It explains their main dynamical ... More


Cohomology of Aubry-Mather type

Kaloshin Vadim and Zhang Ke

in Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom: (AMS-208)

Published in print:
2020
Published Online:
May 2021
ISBN:
9780691202525
eISBN:
9780691204932
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691202525.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter defines cohomology of Aubry-Mather type and explains why it implies one of the diffusion mechanisms, after a generic perturbation. The definition of Aubry-Mather type includes a much ... More


Forcing Relation

Kaloshin Vadim and Zhang Ke

in Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom: (AMS-208)

Published in print:
2020
Published Online:
May 2021
ISBN:
9780691202525
eISBN:
9780691204932
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691202525.003.0002
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter describes forcing relations, different diffusion mechanisms, and Aubry-Mather types. The Aubry set can be decomposed into disjoint invariant sets called static classes, which gives ... More


Aubry-Mather type at the single resonance

Kaloshin Vadim and Zhang Ke

in Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom: (AMS-208)

Published in print:
2020
Published Online:
May 2021
ISBN:
9780691202525
eISBN:
9780691204932
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691202525.003.0009
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter proves Aubry-Mather type in the single-resonance regime. It proves that for a single-resonance normal form system which satisfies the non-degeneracy conditions, every c in the resonance ... More


Aubry-Mather type at the Double Resonance

Kaloshin Vadim and Zhang Ke

in Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom: (AMS-208)

Published in print:
2020
Published Online:
May 2021
ISBN:
9780691202525
eISBN:
9780691204932
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691202525.003.0011
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter proves Aubry-Mather type for the double resonance regime. It begins by considering the “non-critical energy case” and showing that the cohomologies as chosen are of Aubry-Mather type. ... More


View: