Titlebook: Elementary Stability and Bifurcation Theory; Gérard Iooss,Daniel D. Joseph Textbook 1990Latest edition Springer-Verlag Berlin Heidelberg 1

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松紧带

Asymptotic Solutions of Evolution Problems,e - ∞ < µ < ∞. The unknown in (I.1) is U(.). (F.,µ, U) is a given nonlinear function or operator. * When F is independent of . we omit . and write F(µ, U). (I.1) governs the evolution of U(.) from its .(0)= U.. An asymptotic solution is a solution to which U(.) evolves after the transient effects as

Phonophobia

Bifurcation and Stability of Steady Solutions of Evolution Equations in One Dimension,udy of stability and bifurcation to arrange things so that..But we shall not require (II.2). Instead we require that equilibrium solutions of (II.1) satisfy u =., independent of. and. The study of bifurcation of equilibrium solutions of the autonomous problem (II.1)is equivalent to the study of sing

Infect

Imperfection Theory and Isolated Solutions Which Perturb Bifurcation,hod of studying isolated solutions which are close to bifurcating solutions is known as imperfection theory. Some of the basic ideas involved in imperfection theory can be understood by comparing the bending of an initially straight column with an initially imperfect, say bent, column (see Figure II

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吃掉

Bifurcation of Periodic Solutions from Steady Ones (Hopf Bifurcation) in Two Dimensions,urcation of a steady solution. In this case the symmetry of the forcing data, which is steady, is broken by the time-periodic solution. The dynamical system then has “a mind of its own” in the sense that the solution does not follow the symmetry imposed by the given data.

LUCY

Bifurcation of Periodic Solutions in the General Case,applies in R“ and in infinite dimensions; say, for partial differential equations and for functional differential equations, when the steady solution loses stability at a simple, complex-valued eigenvalue. The mathematical analysis is framed in terms of the autonomous evolution equation (VI.45) redu

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