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Mosc. Math. J., 2014, Volume 14, Number 2, Pages 181–203 (Mi mmj519)  

This article is cited in 7 scientific papers (total in 7 papers)

Generic fast diffusion for a class of non-convex Hamiltonians with two degrees of freedom

Abed Bounemouraa, Vadim Kaloshinb

a Université Paris Dauphine, CEREMADE, Place du Marchal de Lattre de Tassigny
b Department of Mathematics, University of Maryland, College Park, MD, 20817

Abstract: In this paper, we study small perturbations of a class of non-convex integrable Hamiltonians with two degrees of freedom, and we prove a result of diffusion for an open and dense set of perturbations, with an optimal time of diffusion which grows linearly with respect to the inverse of the size of the perturbation.

Key words and phrases: Arnold diffusion, linear diffusion, superconductivity channels, Nekhoroshev theory, convexity, resonant normal forms.

DOI: https://doi.org/10.17323/1609-4514-2014-14-2-181-203

Full text: http://www.mathjournals.org/.../2014-014-002-002.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 37J40
Received: June 27, 2013; in revised form November 8, 2013
Language:

Citation: Abed Bounemoura, Vadim Kaloshin, “Generic fast diffusion for a class of non-convex Hamiltonians with two degrees of freedom”, Mosc. Math. J., 14:2 (2014), 181–203

Citation in format AMSBIB
\Bibitem{BouKal14}
\by Abed~Bounemoura, Vadim~Kaloshin
\paper Generic fast diffusion for a~class of non-convex Hamiltonians with two degrees of freedom
\jour Mosc. Math.~J.
\yr 2014
\vol 14
\issue 2
\pages 181--203
\mathnet{http://mi.mathnet.ru/mmj519}
\crossref{https://doi.org/10.17323/1609-4514-2014-14-2-181-203}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3236491}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000342789300002}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. Kaloshin, K. Zhang, “Arnold diffusion for smooth convex systems of two and a half degrees of freedom”, Nonlinearity, 28:8 (2015), 2699–2720  crossref  mathscinet  zmath  isi  elib  scopus
    2. M. B. Gubaidullin, “Commensurability and Molchanov's hypothesis”, Theoret. and Math. Phys., 187:1 (2016), 570–582  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. A. Bounemoura, V. Kaloshin, “A note on micro-instability for Hamiltonian systems close to integrable”, Proc. Amer. Math. Soc., 144:4 (2016), 1553–1560  crossref  mathscinet  zmath  isi  scopus
    4. Abed Bounemoura, “Generic Perturbations of Linear Integrable Hamiltonian Systems”, Regul. Chaotic Dyn., 21:6 (2016), 665–681  mathnet  crossref  mathscinet
    5. S. M. Pittman, E. Tannenbaum, E. J. Heller, “Dynamical tunneling versus fast diffusion for a non-convex Hamiltonian”, J. Chem. Phys., 145:5 (2016), 054303  crossref  isi  scopus
    6. M. Entov, L. Polterovich, “Lagrangian tetragons and instabilities in Hamiltonian dynamics”, Nonlinearity, 30:1 (2017), 13–34  crossref  mathscinet  zmath  isi  scopus
    7. A. Bounemoura, “Some instability properties of resonant invariant tori in Hamiltonian systems”, Math. Res. Lett., 24:1 (2017), 21–35  crossref  mathscinet  zmath  isi
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