By Paul H. Rabinowitz
The papers during this quantity signify the lawsuits of the complicated Seminar on purposes of Bifurcation idea held in Madison on October 27-29, 1976. except for the survey by means of M. G. Crandall, the papers are released within the order within which they're provided.
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Extra info for Applications of bifurcation theory: proceedings of an advanced seminar
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Qm ) is a set of parameters. This equation determines a set of solutions, each specified by their initial values. We can specify the solution corresponding to the initial condition p by x(t; p). Consider a set of initial conditions contained in a vanishing small volume V . 1), the volume will change as a function of t. Precisely, dV = dt m ··· V i=1 ∂gi ∂xi dx1 · · · dxn . The summation term is the generalized divergence of g and is called the Lie derivative. Dissipative systems are characterized by contracting volumes; this is equivalent to dV /dt < 0.
The point at infinity is classified by changing variables to t = x−1 and then analyzing the point t = 0. See page 403. Singular solution A singular solution is a solution of a differential equation that is not derivable from the general solution by any choice of the arbitrary constants appearing in the general solution. Only nonlinear equations have singular solutions. See page 623. Stability The solution to a differential equation is said to be stable if small perturbations in the initial conditions, boundary conditions, or coefficients in the equation itself lead to “small” changes in the solution.
Applications of bifurcation theory: proceedings of an advanced seminar by Paul H. Rabinowitz