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008 131112s2001 xxu| s |||| 0|eng d
020 _a9781461300038
_9978-1-4613-0003-8
082 _a515
_223
100 _aPerko, Lawrence.
_920164
245 _aDifferential Equations and Dynamical Systems
_h[electronic resource] /
_cby Lawrence Perko.
250 _a3rd ed. 2001.
260 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2001.
300 _aXIV, 557 p. 11 illus.
_bonline resource.
505 _aSeries Preface -- Preface to the Third Edition -- Linear Systems -- Nonlinear Systems: Local Theory -- Nonlinear Systems: Global Theory -- Nonlinear Systems: Bifurcation Theory -- References -- Additional References -- Index.
520 _a 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.
650 _aMathematical analysis.
_920165
650 _aContinuum mechanics.
_920166
650 _aMechanics.
_920167
650 _aAnalysis.
_920168
650 _aContinuum Mechanics.
_920169
650 _aClassical Mechanics.
_920170
856 _uhttps://doi.org/10.1007/978-1-4613-0003-8
942 _cEBK
999 _c13611
_d13611