CHAOS.bib

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@ARTICLE{jauslin2002renormalization,
  AUTHOR = {C. Chandre and H. R. Jauslin},
  TITLE = {Renormalization-group analysis for the transition to
                  chaos in Hamiltonian systems},
  JOURNAL = {Physics Reports},
  YEAR = {2002},
  VOLUME = {365},
  NUMBER = {1},
  PAGES = {1-64},
  MONTH = {July},
  ROPSECTIONS = {RG CHAOS},
  PDF = {/sci_docs/physics/papers/PhysRep/jauslin2002renormalization.pdf},
  ABSTRACT = {We study the stability of Hamiltonian systems in
                  classical mechanics with two degrees of freedom by
                  renormalization-group methods. One of the key
                  mechanisms of the transition to chaos is the
                  break-up of invariant tori, which plays an essential
                  role in the large scale and long-term behavior. The
                  aim is to determine the threshold of break-up of
                  invariant tori and its mechanism. The idea is to
                  construct a renormalization transformation as a
                  canonical change of coordinates, which deals with
                  the dominant resonances leading to qualitative
                  changes in the dynamics. Numerical results show that
                  this transformation is an efficient tool for the
                  determination of the threshold of the break-up of
                  invariant tori for Hamiltonian systems with two
                  degrees of freedom. The analysis of this
                  transformation indicates that the break-up of
                  invariant tori is a universal mechanism. The
                  properties of invariant tori are described by the
                  renormalization flow. A trivial attractive set of
                  the renormalization transformation characterizes the
                  Hamiltonians that have a smooth invariant torus. The
                  set of Hamiltonians that have a non-smooth invariant
                  torus is a fractal surface. This critical surface is
                  the stable manifold of a single strange set
                  encompassing all irrational frequencies. This
                  hyperbolic strange set characterizes the
                  Hamiltonians that have an invariant torus at the
                  threshold of the break-up. From the critical strange
                  set, one can deduce the critical properties of the
                  tori (self-similarity, universality classes).}
}


@ARTICLE{Vollmer2002chaos,
  AUTHOR = {J\"{u}rgen Vollmer},
  TITLE = {Chaos, spatial extension, transport, and non-equilibrium thermodynamics },
  JOURNAL = {Physics Reports },
  YEAR = {2002},
  VOLUME = {372},
  NUMBER = {2},
  PAGES = {131-267},
  ROPSECTIONS = {CHAOS},
  PDF = {/sci_docs/physics/papers/RepProgPhys/Vollmer2002chaos.pdf},
  ABSTRACT = {The connection between the thermodynamic description of
  transport phenomena and a microscopic description of the underlying
  chaotic motion has recently received new attention due to the
  convergence of ongoing developments in the theory of deterministic
  chaotic systems, in the foundation of non-equilibrium statistical
  physics and of non-equilibrium molecular dynamics simulations. An
  overview of these developments is given with an emphasis on explicit
  calculations on exactly solvable models, that may serve as paradigms
  for this approach to model transport. }
}

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@BOOK{prigogine1996fin,
  AUTHOR = {Ilya Prigogine},
  ALTEDITOR = {},
  TITLE = {La fin des certitudes},
  PUBLISHER = {Poches Odile Jacob},
  YEAR = {1996},
  ROPSECTIONS = {CHAOS}
}