% IMPORTANT: The following is UTF-8 encoded.  This means that in the presence
% of non-ASCII characters, it will not work with BibTeX 0.99 or older.
% Instead, you should use an up-to-date BibTeX implementation like “bibtex8” or
% “biber”.

@ARTICLE{DiCairano:904541,
      author       = {Di Cairano, Loris and Gori, Matteo and Pettini, Giulio and
                      Pettini, Marco},
      title        = {{H}amiltonian chaos and differential geometry of
                      configuration space–time},
      journal      = {Physica / D},
      volume       = {422},
      issn         = {0167-2789},
      address      = {Amsterdam [u.a.]},
      publisher    = {Elsevier},
      reportid     = {FZJ-2021-06111},
      pages        = {132909 -},
      year         = {2021},
      abstract     = {This paper tackles Hamiltonian chaos by means of elementary
                      tools of Riemannian geometry. More precisely, a Hamiltonian
                      flow is identified with a geodesic flow on configuration
                      space–time endowed with a suitable metric due to
                      Eisenhart. Until now, this framework has never been given
                      attention to describe chaotic dynamics. A gap that is filled
                      in the present work. In a Riemannian-geometric context, the
                      stability/instability of the dynamics depends on the
                      curvature properties of the ambient manifold and is
                      investigated by means of the Jacobi–Levi-Civita (JLC)
                      equation for geodesic spread. It is confirmed that the
                      dominant mechanism at the ground of chaotic dynamics is
                      parametric instability due to curvature variations along the
                      geodesics. A comparison is reported of the outcomes of the
                      JLC equation written also for the Jacobi metric on
                      configuration space and for another metric due to Eisenhart
                      on an extended configuration space–time. This has been
                      applied to the Hénon–Heiles model, a two-degrees of
                      freedom system. Then the study has been extended to the 1D
                      classical Heisenberg model at a large number of degrees of
                      freedom. Both the advantages and drawbacks of this
                      geometrization of Hamiltonian dynamics are discussed.
                      Finally, a quick hint is put forward concerning the possible
                      extension of the differential–geometric investigation of
                      chaos in generic dynamical systems, including dissipative
                      ones, by resorting to Finsler manifolds.},
      cin          = {IAS-5 / INM-9},
      ddc          = {530},
      cid          = {I:(DE-Juel1)IAS-5-20120330 / I:(DE-Juel1)INM-9-20140121},
      pnm          = {899 - ohne Topic (POF4-899)},
      pid          = {G:(DE-HGF)POF4-899},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000642478400001},
      doi          = {10.1016/j.physd.2021.132909},
      url          = {https://juser.fz-juelich.de/record/904541},
}