View:

- no detail
- some detail
- full detail

## 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:

- no detail
- some detail
- full detail