Dynamical Stability in Lagrangian Systems

@article{Boyland1999DynamicalSI,
  title={Dynamical Stability in Lagrangian Systems},
  author={Philip Boyland and Christopher Gol'e},
  journal={arXiv: Dynamical Systems},
  year={1999},
  pages={90-114}
}
The first part of this paper surveys results on time-periodic Lagrangian systems on a hyperbolic manifolds. Results of the authors show that the dynamics of such systems are, in a precise sense, at least as complicated as those of the geodesic flow of the hyperbolic metric. The second part of the paper presents original results on autonomous Lagrangian systems on the two torus including a precise description of Mather’s beta function. Examples are given of mechanical systems with non-strictly… 

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Complicated dynamics from simple topological hypotheses
  • R. MacKay
  • Biology, Mathematics
    Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
  • 2001
TLDR
A diverse range of more sophisticated examples of dynamical system for which quite simple topological hypotheses imply very complicated behaviour are produced and their relevance to physical applications is explored.

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