COMPLEX DYNAMICS AND STATISTICS OF 1-D HAMILTONIAN LATTICES: LONG RANGE INTERACTIONS AND SUPRATRANSMISSION
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Date
2019
Authors
Bountis, Anastasios
Journal Title
Journal ISSN
Volume Title
Publisher
Nonlinear Phenomena in Complex Systems
Abstract
In this paper, I review a number of results that my co-workers and I have obtained in
the field of 1–Dimensional (1D) Hamiltonian lattices. This field has grown in recent years,
due to its importance in revealing many phenomena that concern the occurrence of chaotic
behavior in conservative physical systems with a high number of degrees of freedom. After the
establishment of the Kolomogorov–Arnol’d–Moser (KAM) theory in the 1960s, a wealth of
results were obtained about such systems as small perturbations of completely integrable N degree-of-freedom Hamiltonians, where ordered motion is dominant in the form of invariant
tori. Since the 1980s, however, and particularly in the last two decades, there has been
great progress in understanding the properties of Hamiltonian 1D lattices far from the KAM
regime, where "weak" and "strong" forms of chaos begin to play an increasingly significant
role. It is the purpose of this review to address and highlight some of these advances, in
which the author has made several contributions concerning the dynamics and statistics of
these lattices
Description
Keywords
Type of access: Open Access, N-degree-of-freedom Hamiltonian system, dynamics, statistics
Citation
Bountis, A. (2020). Complex Dynamics and Statistics of 1-D Hamiltonian Lattices: Long Range Interactions and Supratransmission. Nonlinear Phenomena in Complex Systems, 23(2), 133–148. https://doi.org/10.33581/1561-4085-2020-23-2-133-148