Applied Equivariant Degree (Differential Equations & Dynamical Systems) - Hardcover

Zalman Balanov; Wieslaw Krawcewicz; Heinrich Steinlein

Hardcover

ISBN 10: 1601330014 ISBN 13: 9781601330017

Publisher: American Institute of Mathematical Sciences, 2006

Synopsis

The book is a self-contained comprehensive exposition of the equivariant degree theory and its applications to a variety of problems arising in physics, chemistry, biology and engineering. This monograph presents the theoretical foundations, construction, and the fundamental properties of the equivariant degree and its practical variations, which are applied to a series of examples from (functional) differential equations. It contains a) the first thorough and complete introduction up to the present state of art to equivariant degree theory including non-abelian actions, and b) provides for the first time several computer routines allowing an effective practical computation of the degree, illustrated by numerous concrete examples and charts. The exposition of the material is mainly addressed to experienced researchers and graduate students interested in applications of equivariant topological methods, or working with differential equations and their applications, like physicists, biologists, chemists and engineers dealing with nonlinear dynamics with symmetries.

About this title

About the Author

Zalman Balanov received his PhD from Belorussian State University, USSR, in 1989. After staying at Heidelberg and Munich Universities as the Alexander von Humboldt Fellow, he worked several years at Bar Ilan University (Israel). Currently, he is a Professor of Mathematics at Netanya Academic College (Israel). He is the author of about 50 publications (including 2 monographs) in the areas of Equivariant Nonlinear Analysis, Equivariant Topology, Nonassociative Algebras, and Numerical Analysis. His main contributions in Equivariant Analysis and Topology are related to: equivariant homotopy theory (especially, degree theory), dynamical systems with symmetries (including the models of natural phenomena appearing in mathematical biology, fluid mechanics, transmission lines), variational problems with symmetries (Lusternik-Schnirelman Theory, Morse-Floer Theory, Elasticity Theory), bifurcation theory (especially, Hopf bifurcation phenomenon). In the series of recent papers on nonassociative algebras (joint work with Y. Krasnov), they discovered unexpected connections between algebra, topology, analysis, dynamical systems, and invariant theory. Wieslaw Krawcewicz obtained his PhD degree in 1985 from l'Universite de Montreal in the area of nonlinear analysis. After completing his postdoctoral fellowship at l'Universite Catholique de Lovain at Lovain-la-Neuve in Belgium (1986-1987), he moved to Edmonton, where in 1988 he joined the faculty in the Department of Mathematics at the University of Alberta. He presently continues to work as Professor at the University of Alberta. In 1993/1994 he was the Alexander von Humboldt fellow at the University of Wuerzburg (in Germany) and, in the subsequent years, from 1996 till 2008, he was recurrently returning to Ludwig-Maximillians-Universitat in Munich, where he continued his Humboldt fellowship and the collaborative research with Zalman Balanov and Heinrich Steinlein. Wieslaw Krawcewicz is an author of more than 50 research papers and another monograph: Theory of Degrees with Applications to Bifurcations and Differential Equations (written with J. Wu and published by John Wiley and Sons in 1997). His primary area of interest is related to various topics in the Topological Equivariant Nonlinear Analysis. In particular, his work is devoted to developments of various equivariant degree theories (for non-abelian compact Lie groups), usage of axiomatic approach, and computer software, and their applications to differential equations (ODEs/FDEs/PDEs/FPDEs) such as stydying symmetric Hopf bifurcation in ODEs, FDEs, PDEs and FPDEs in concrete models related to applications in mathematical biology, robotics and medicine. He is also interested in degree-theoretical approach to detect periodic solutions in autonomous differential systems. Heinrich Steinlein received his doctoral and habilitation degrees from the University of Munich, where he now teaches as a professor of mathematics. His research interests are in nonlinear functional analysis and dynamical systems with particular focus on the Borsuk antipodal theorem and (equivariant) degree theory.

Edition details

• Publisher: American Institute of Mathematical Sciences
• Publication date: 2006
• Language: English
• ISBN 10: 1601330014
• ISBN 13: 9781601330017
• Binding: Hardcover
• Edition number: 1
• Number of pages: 552
• Editor: Jianhong Wu, Jerry L. Bona, Hans G. Othmer, Jeff Webb, Messoud Efendiev, Yacine Chitour