Although this systematic study of autonomous systems begins with a thorough treatment of linear systems, the main emphasis is on local and global behavior of nonlinear systems. The main purpose of this revised edition is to introduce students to the qualitative and geometric theory of ordinary differential equations as well as serving as a reference book for mathematicians researching dynamical systems. Readers will find that, except for certain topics of current mathematical research, such as the number of limit cycles and the nature of attracting sets of dynamical systems, the global qualitative theory of a nonlinear dynamical system leads to an understanding of the solution set of the nonlinear system to rival that which we have of linear flows.
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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 Poincare 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.Review:
Reviews from the first edition:
“...The text succeeds admiraby ... Examples abound, figures are used to advantage, and a reasonable balance is maintained between what is proved in detail and what is asserted with supporting references ... Each section closes with a set of problems, many of which are quite interesting and round out the text material ... this book is to be highly recommended both for use as a text, and for professionals in other fields wanting to gain insight into modern aspects of the geometric theory of continuous (i.e., not discrete) dynamical systems.” MATHEMATICAL REVIEWS
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Descripción Springer, 1990. Estado de conservación: New. 407 pp., Hardcover, NEW!!. Nº de ref. de la librería ZB1080734
Descripción Springer. Estado de conservación: New. Nº de ref. de la librería 5551477
Descripción Springer, 1993. Hardcover. Estado de conservación: New. book. Nº de ref. de la librería M0387974431
Descripción Springer, 1993. Hardcover. Estado de conservación: New. Never used!. Nº de ref. de la librería P110387974431
Descripción Springer. Hardcover. Estado de conservación: New. 0387974431 New Condition. Nº de ref. de la librería NEW7.0128254