Effective Hamiltonians and averaging for Hamiltonian dynamics II

L. C. Evans; D. Gomes

doi:10.1007/s002050100181

Effective Hamiltonians and averaging for Hamiltonian dynamics II

L. C. Evans^*, D. Gomes

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

31 Scopus citations

Abstract

We extend to time-dependent Hamiltonians some of the PDE methods from our previous paper [E-G1], and in particular the theory of "effective Hamiltonians" introduced by LIONS, PAPANICOLAOU & VARADHAN [L-P-V]. These PDE techniques augment the variational approach of MATHER [Mt1,Mt2,Mt3,Mt4,M-F] and the weak KAM methods of FATHI [F1,F2,F3,F4,F5]. We also provide a weak interpretation of adiabatic invariance of the action and suggest a formula for the Berry-Hannay geometric phase in terms of an effective Hamiltonian.

Original language	English (US)
Pages (from-to)	271-305
Number of pages	35
Journal	Archive for Rational Mechanics and Analysis
Volume	161
Issue number	4
DOIs	https://doi.org/10.1007/s002050100181
State	Published - Mar 2002
Externally published	Yes

ASJC Scopus subject areas

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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title = "Effective Hamiltonians and averaging for Hamiltonian dynamics II",

abstract = "We extend to time-dependent Hamiltonians some of the PDE methods from our previous paper [E-G1], and in particular the theory of {"}effective Hamiltonians{"} introduced by LIONS, PAPANICOLAOU & VARADHAN [L-P-V]. These PDE techniques augment the variational approach of MATHER [Mt1,Mt2,Mt3,Mt4,M-F] and the weak KAM methods of FATHI [F1,F2,F3,F4,F5]. We also provide a weak interpretation of adiabatic invariance of the action and suggest a formula for the Berry-Hannay geometric phase in terms of an effective Hamiltonian.",

author = "Evans, {L. C.} and D. Gomes",

year = "2002",

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doi = "10.1007/s002050100181",

language = "English (US)",

volume = "161",

pages = "271--305",

journal = "Archive for Rational Mechanics and Analysis",

issn = "0003-9527",

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TY - JOUR

T1 - Effective Hamiltonians and averaging for Hamiltonian dynamics II

AU - Evans, L. C.

AU - Gomes, D.

PY - 2002/3

Y1 - 2002/3

N2 - We extend to time-dependent Hamiltonians some of the PDE methods from our previous paper [E-G1], and in particular the theory of "effective Hamiltonians" introduced by LIONS, PAPANICOLAOU & VARADHAN [L-P-V]. These PDE techniques augment the variational approach of MATHER [Mt1,Mt2,Mt3,Mt4,M-F] and the weak KAM methods of FATHI [F1,F2,F3,F4,F5]. We also provide a weak interpretation of adiabatic invariance of the action and suggest a formula for the Berry-Hannay geometric phase in terms of an effective Hamiltonian.

AB - We extend to time-dependent Hamiltonians some of the PDE methods from our previous paper [E-G1], and in particular the theory of "effective Hamiltonians" introduced by LIONS, PAPANICOLAOU & VARADHAN [L-P-V]. These PDE techniques augment the variational approach of MATHER [Mt1,Mt2,Mt3,Mt4,M-F] and the weak KAM methods of FATHI [F1,F2,F3,F4,F5]. We also provide a weak interpretation of adiabatic invariance of the action and suggest a formula for the Berry-Hannay geometric phase in terms of an effective Hamiltonian.

UR - http://www.scopus.com/inward/record.url?scp=0036525374&partnerID=8YFLogxK

U2 - 10.1007/s002050100181

DO - 10.1007/s002050100181

M3 - Article

AN - SCOPUS:0036525374

SN - 0003-9527

VL - 161

SP - 271

EP - 305

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

IS - 4

ER -

Effective Hamiltonians and averaging for Hamiltonian dynamics II

Abstract

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