Complex Dynamics and Statistics in Hamiltonian 1-Dimensional Lattices

  • A. Bountis School of Science and Technology, Department of Mathematics, Nazarbayev University, Astana, Kazakhstan

Abstract

In this paper I review in a brief and introductory way some important developments in the analysis of the dynamics and statistics of N – dimensional Hamiltonian systems, in which my research team and I have played an important role over the last two decades. The results I describe here have helped us understand the surprising importance of simple periodic orbits and their local stability properties in revealing crucial dynamical and statistical properties of the systems as a whole. This has led us to introduce the concepts of “strong” and “weak” chaos that are expected to play a significant role in better understanding the complexity of these multi-dimensional systems, which have important applications in solid state, field theory, superconductivity and more recently nonlinear optics.

 
 


 
 
 


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Published
Dec 29, 2018
How to Cite
BOUNTIS, A.. Complex Dynamics and Statistics in Hamiltonian 1-Dimensional Lattices. International Journal of Mathematics and Physics, [S.l.], v. 9, n. 2, p. 21-42, dec. 2018. ISSN 2409-5508. Available at: <http://ijmph.kaznu.kz/index.php/kaznu/article/view/261>. Date accessed: 21 mar. 2019.