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This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman - Grobman theorem, the use of the Poincaré map in the theory of limit cycles, the theory of rotated vector fields and its use in the study of limit cycles and homoclinic loops, and a description of the behavior and termination of one-parameter families of limit cycles. In addition to minor corrections and updates throughout, this new edition contains materials on higher order Melnikov functions and the bifurcation of limit cycles for planar systems of differential equations, including new sections on Francoise's algorithm for higher order Melnikov functions and on the finite codimension bifurcations that occur in the class of bounded quadratic systems.

...iel Lecture Notes: AntonisPapachristodoulou Department of Engineering Science University of Oxford Dynamical Systems: Lecture 1 1 ... Differential equations, dynamical systems, and an ... ... . Lecture 1: Introduc.on •We will study the topological propertiesof solutions of ordinary differential equationswithoutsolving them •Essentially about the geometry of the paths ... To study dynamical systems mathematically, we represent them in terms of differential equations. The state of dynamical system at an instant of time is described by a point in an n-dimensional space called the state space (th ... Amazon.fr - Nonlinear Differential Equations and Dynamical ... ... . The state of dynamical system at an instant of time is described by a point in an n-dimensional space called the state space (the dimension n depends on how complicated the systems is - for the double pendulum below, n=4). This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the ... Dynamical systems theory is an area of mathematics used to describe the behavior of the complex dynamical systems, usually by employing differential equations or difference equations.When differential equations are employed, the theory is called continuous dynamical systems.From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a generalization ......