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algebraic Anal analysis apply assume asymptotic behavior attractor Backlund transformation Banach space Berlin Heidelberg 1987 Bifurcation Theory bounded bounded set Chow compact Computer confinor consider constant continuous continuous function convergence corresponding curve defined denote derivatives Dimensional Systems Edited dynamical system Dynamics of Infinite Edited by S.-N eigenvalues eigenvector equilibrium example exists exponential F37 Dynamics finite fixed point functional differential equations geodesic flow given global Hamilton-Jacobi equations Hopf bifurcation implies Infinite Dimensional Systems integral interval invariant manifolds invariant set iteration J. K. Hale Lax pair Lemma Liapunov function linear matrix methods metric neighborhood nonlinear nonnegative obtain operator Parabolic parameter periodic orbits periodic solutions perturbation polynomial positive problem proof properties Proposition prove result satisfies scalar semiflow semigroup semilinear sequence Springer-Verlag Berlin Heidelberg stable subspace symmetry Theorem 2.1 theory tion trajectory unique unstable manifold vector field viscosity solutions wave zero