Jump to ContentJump to Main Navigation

You are looking at 1-5 of 5 items

  • Keywords: forcing equivalence x
Clear All Modify Search

View:

Double Resonance: Forcing Equivalence

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/9780691202525.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter assesses the choice of cohomology and Aubry-Mather type at the double resonance. It begins by choosing cohomology classes for the (unperturbed) slow mechanical system. As in the case of ... 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


Forcing equivalence between kissing cylinders

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/9780691202525.003.0012
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter formulates and proves the jump mechanism. It constructs a variational problem which proves forcing equivalence for the original Hamiltonian using Definition 6.18. It first constructs a ... More


Normal Forms and Cohomology Classes at Single Resonances

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/9780691202525.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses the single-resonance non-degeneracy conditions and normal forms. It then formulates Theorem 3.3, which covers the forcing equivalence in the single-resonance regime. The ... More


Perturbative weak KAM theory

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/9780691202525.003.0007
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter explores perturbation aspects of the weak Kolmogorov-Arnold-Moser (KAM) theory. By perturbative weak KAM theory, we mean two things. How do the weak KAM solutions and the Mather, Aubry, ... More


View: