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Jan Awrejcewicz, Mariusz M. Holicke “Smooth and Nonsmooth High Dimensional Chaos and the Melnidov-Type Methods"

This book focuses on the development of Melnikov-type methods applied to high dimensional dynamical systems governed by ordinary differential equations. Although the classical Melnikov's technique has found various applications in predicting homoclinic intersections, it is devoted only to the analysis of three-dimensional systems (in the case of mechanics, they represent one-degree-of-freedom nonautonomous systems). This book extends the classical Melnikov's approach to the study of high dimensional dynamical systems, and uses simple models of dry friction to analytically predict the occurrence of both stick-slip and slip-slip chaotic orbits, research which is very rarely reported in the existing literature even on one-degree-of-freedom nonautonomous dynamics.

This pioneering attempt to predict the occurrence of deterministic chaos of nonlinear dynamical systems will attract many researchers including applied mathematicians, physicists, as well as practicing engineers. Analytical formulas are explicitly formulated step-by-step, even attracting potential readers without a rigorous mathematical background.

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	Science/Engineering Nonsmooth Equations in Optimization: Regularity, Calculus, Methods and Applications Nonsmooth Equations in Optimization: Regularity, Calculus, Methods and ApplicationsSpringer \| May 31, 2002 \| ISBN: 1402005504 \| 360 pages \| PDF \| 3.91 mbThe book establishes links between regularity and derivative concepts of nonsmooth anal ...
	Science/Engineering Smooth and Nonsmooth High Dimensional Chaos and the Melnidov-Type Methods (repost) Smooth and Nonsmooth High Dimensional Chaos and the Melnidov-Type Methods World Scientific Publishing Company \| 2007-09-21 \| ISBN: 9812709096 \| 320 pages \| PDF \| 9,4 MBThis book focuses on the development of Melnikov-type methods applied to ...
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