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Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems by Michal Feckan (Comenius University in Bratislava, Faculty of Mathematics, Physics and Informatics, Department of Mathematical Analysis and Numerical Mathematics, Bratislava, Slovak Republic) at Abbey's Bookshop,
Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems
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Michal Feckan (Comenius University in Bratislava, Faculty of Mathematics, Physics and Informatics, Department of Mathematical Analysis and Numerical Mathematics, Bratislava, Slovak Republic) Michal Pospíšil (Slovak Academy of Sciences, Mathematical Institute, Bratislava, Slovakia)

Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems

Michal Feckan (Comenius University in Bratislava, Faculty of Mathematics, Physics and Informatics, Department of Mathematical Analysis and Numerical Mathematics, Bratislava, Slovak Republic),  Michal Pospíšil (Slovak Academy of Sciences, Mathematical Institute, Bratislava, Slovakia)

$126.95

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English
Academic Press Inc
17 May 2016
Real analysis, real variables
Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems is devoted to the study of bifurcations of periodic solutions for general n-dimensional discontinuous systems. The authors study these systems under assumptions of transversal intersections with discontinuity-switching boundaries. Furthermore, bifurcations of periodic sliding solutions are studied from sliding periodic solutions of unperturbed discontinuous equations, and bifurcations of forced periodic solutions are also investigated for impact systems from single periodic solutions of unperturbed impact equations. In addition, the book presents studies for weakly coupled discontinuous systems, and also the local asymptotic properties of derived perturbed periodic solutions.

The relationship between non-smooth systems and their continuous approximations is investigated as well. Examples of 2-, 3- and 4-dimensional discontinuous ordinary differential equations and impact systems are given to illustrate the theoretical results. The authors use so-called discontinuous Poincaré mapping which maps a point to its position after one period of the periodic solution. This approach is rather technical, but it does produce results for general dimensions of spatial variables and parameters as well as the asymptotical results such as stability, instability, and hyperbolicity.
By:   , , , ,
Imprint:   Academic Press Inc
Country of Publication:   United States
Dimensions:   Height: 235mm,  Width: 191mm,  Spine: 16mm
Weight:   1.040kg
ISBN:   9780128042946
ISBN 10:   012804294X
Pages:   260
Publication Date:  
Audience:   Professional and scholarly ,  Undergraduate
Format:   Hardback
Publisher's Status:   Active

Professor Michal Feckan works at the Department of Mathematical Analysis and Numerical Mathematics at the Faculty of Mathematics, Physics, and Informatics at Comenius University. He specializes in nonlinear functional analysis, and dynamic systems and their applications. There is much interest in his contribution to the analysis of solutions of equations with fractional derivatives. Feckan has written several scientific monographs that have been published at top international publishing houses Michal Pospíšil is senior researcher at the Mathematical Institute of Slovak Academy of Sciences in Bratislava, Slovak Republic. He obtained his Ph.D. (applied mathematics) from the Mathematical Institute of Slovak Academy of Sciences in Bratislava, Slovak Republic. He is interested in discontinuous dynamical systems and delayed differential equations.

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