By Lawrence Perko
This textbook provides a scientific research of the qualitative and geometric conception of nonlinear differential equations and dynamical structures. even supposing the most subject of the ebook is the neighborhood and international habit of nonlinear platforms and their bifurcations, a radical therapy of linear structures is given before everything of the textual content. the entire fabric priceless for a transparent realizing of the qualitative habit of dynamical platforms is contained during this textbook, together with an overview of the facts and examples illustrating the evidence of the Hartman-Grobman theorem, using the Poincare map within the idea of restrict cycles, the speculation of circled vector fields and its use within the examine of restrict cycles and homoclinic loops, and an outline of the habit and termination of one-parameter households of restrict cycles. as well as minor corrections and updates all through, this new version contains fabrics on better order Melnikov idea and the bifurcation of restrict cycles for planar structures of differential equations, together with new sections on Francoise's set of rules for better order Melnikov capabilities and at the finite codimension bifurcations that happen within the type of bounded quadratic platforms.
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