Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 2 min ago
PreprintCC BY-NC-ND 4.0arXiv

Adiabatic Invariant Actions for Partially Integrable Systems

  • Amir Khodaeian Karim
  • Konstantinos Kourliouros
  • Dmitry Turaev
Open at sourcePDFDOICite

Abstract

We introduce action integrals for partially integrable Hamiltonian systems that interpolate between the non-integrable and completely integrable theory. We show that under the assumption of ergodicity of the Hamiltonian system on the common level sets of its integrals, these actions become constants of motion for the averaged dynamics and, consequently, adiabatic invariants when the Hamiltonian function is allowed to slowly change with time.

Related

  1. PAC-Bayesian Bounds for Learning Partially Observed Stochastic Linear Time-Invariant State-Space Systems with Inputs and Sub-Gaussian Noise
    Mihaly Petreczky, Mohamad Al Ahdab, John Leth
    arXivPreprintCC BY 4.0Full textOptimisation & controlarXiv
  2. The ABC-equation revisited: missed (quasi) integrable cases. Part II: extensions and actions
    I. S. Krasil'shchik
    arXivPreprintCC BY 4.0Full textGeometry & topologyMathematical physicsarXiv
  3. Localized oscillations of an Euler--Bernoulli beam with time-varying parameters on a visco-elastic foundation: asymptotics, adiabatic invariant, and equivalent Hamiltonian system
    Ekaterina V. Shishkina, Serge N. Gavrilov, Yulia A. Mochalova
    arXivPreprintCC BY-NC-ND 4.0Full textMathematical physicsGeneral physicsarXiv
  4. Gravity from Invariant Weyl-Integrable space-time (IWIST)
    José Edgar Madriz Aguilar, A. Bernal, M. Montes +1
    arXivPreprintarXiv licenceFull textSolar & stellar physicsMathematical physicsarXiv
  5. A Note on Partially Anti-invariant Submanifolds of Kenmotsu Manifolds
    Muhammad Shuaib, Cenap Ozel, Meraj A. Khan +1
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv

Cite

BibTeXRIS
BibTeX
@misc{karim2026adiabatic,
  title = {{Adiabatic Invariant Actions for Partially Integrable Systems}},
  author = {Amir Khodaeian Karim and Konstantinos Kourliouros and Dmitry Turaev},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.38961},
  eprint = {2609.38961},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.38961},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Adiabatic Invariant Actions for Partially Integrable Systems
AU  - Amir Khodaeian Karim
AU  - Konstantinos Kourliouros
AU  - Dmitry Turaev
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.38961
UR  - https://arxiv.org/abs/2609.38961
AB  - We introduce action integrals for partially integrable Hamiltonian systems that interpolate between the non-integrable and completely integrable theory. We show that under the assumption of ergodicity of the Hamiltonian system on the common level sets of its integrals, these actions become constants of motion for the averaged dynamics and, consequently, adiabatic invariants when the Hamiltonian function is allowed to slowly change with time.
ER  -