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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


Variational Aspects Of The Slow Mechanical System

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/9780691202525.003.0015
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter describes the variational property of the slow mechanical system. The main goal is to derive some properties of the “channel” and information about the Aubrey sets. More precisely, the ... More


Double Resonance: Geometric Description

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/9780691202525.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter examines the geometrical structure for the system at double resonance. After describing the normal form near a double resonance, it reduces the system to the slow mechanical system with ... More


Generic properties of mechanical systems on the two-torus

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/9780691202525.003.0013
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter focuses on proving generic properties of the minimizing orbits of the slow mechanical system. It first proves Theorem 4.5 concerning non-critical but bounded energy, before proving ... More


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


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