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Author : Konstantinos Efstathiou
Release : 2005
Genre : Hamiltonian systems
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Metamorphoses of Hamiltonian Systems with Symmetries by : Konstantinos Efstathiou
Download or read book Metamorphoses of Hamiltonian Systems with Symmetries written by Konstantinos Efstathiou. This book was released on 2005. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Konstantinos Efstathiou
Release : 2005
Genre : Hamiltonian systems
Kind : eBook
Book Rating : 168/5 ( reviews)
Book Synopsis Metamorphoses of Hamiltonian Systems with Symmetries by : Konstantinos Efstathiou
Download or read book Metamorphoses of Hamiltonian Systems with Symmetries written by Konstantinos Efstathiou. This book was released on 2005. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Valerij V. Kozlov
Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 937/5 ( reviews)
Book Synopsis Symmetries, Topology and Resonances in Hamiltonian Mechanics by : Valerij V. Kozlov
Download or read book Symmetries, Topology and Resonances in Hamiltonian Mechanics written by Valerij V. Kozlov. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: John Hornstein has written about the author's theorem on nonintegrability of geodesic flows on closed surfaces of genus greater than one: "Here is an example of how differential geometry, differential and algebraic topology, and Newton's laws make music together" (Amer. Math. Monthly, November 1989). Kozlov's book is a systematic introduction to the problem of exact integration of equations of dynamics. The key to the solution is to find nontrivial symmetries of Hamiltonian systems. After Poincaré's work it became clear that topological considerations and the analysis of resonance phenomena play a crucial role in the problem on the existence of symmetry fields and nontrivial conservation laws.
Author : Heinz Hanßmann
Release : 2006-10-18
Genre : Mathematics
Kind : eBook
Book Rating : 966/5 ( reviews)
Book Synopsis Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems by : Heinz Hanßmann
Download or read book Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems written by Heinz Hanßmann. This book was released on 2006-10-18. Available in PDF, EPUB and Kindle. Book excerpt: This book demonstrates that while elliptic and hyperbolic tori determine the distribution of maximal invariant tori, they themselves form n-parameter families. Therefore, torus bifurcations of high co-dimension may be found in a single given Hamiltonian system, absent untypical conditions or external parameters. The text moves logically from the integrable case, in which symmetries allow for reduction to bifurcating equilibria, to non-integrability, where smooth parametrisations must be replaced by Cantor sets.
Author : Robert A. Meyers
Release : 2011-10-05
Genre : Mathematics
Kind : eBook
Book Rating : 054/5 ( reviews)
Book Synopsis Mathematics of Complexity and Dynamical Systems by : Robert A. Meyers
Download or read book Mathematics of Complexity and Dynamical Systems written by Robert A. Meyers. This book was released on 2011-10-05. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
