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Conclusions, Open Problems and Future Outlook

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Book cover Complex Hamiltonian Dynamics

Part of the book series: Springer Series in Synergetics ((SSSYN,volume 10))

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Abstract

The final Chapter first summarizes and discusses the main conclusions described in the book. We then list a number of open problems, which we feel should be further pursued in continuation of what we have presented in earlier Chapters. We start with some recent results that extend the mathematical theory of integrability from the viewpoint of singularity analysis and continue with some directions that further develop the topics of nonlinear normal modes, localization, diffusion and the complex statistical properties of nonlinear lattices. Finally, regarding the future outlook of research in Hamiltonian dynamics, we briefly review three topics of great current interest that were not treated in the book, but are extremely important in view of their far-reaching experimental applications: (1) anomalous heat conduction and the discovery of mechanisms that control heat flow based on the dynamics of Hamiltonian lattices, (2) soliton dynamics in nonlinear photonic structures and (3) kinetic theory of Hamiltonian systems with applications to plasma physics.

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  1. Department of Mathematics, University of Patras, Patras, Greece

    Tassos Bountis

  2. MPI for the Physics of Complex Systems, Dresden, Germany

    Haris Skokos

  3. Physics Department, Aristotle University of Thessaloniki, Thessaloniki, Greece

    Haris Skokos

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Bountis, T., Skokos, H. (2012). Conclusions, Open Problems and Future Outlook. In: Complex Hamiltonian Dynamics. Springer Series in Synergetics, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27305-6_9

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