ELEMENTS OF DIFFERENTIABLE DYNAMICS AND BIFURCATION THEORY

By E. ALARS

CONTENTS NONAUTONOMOUS DYNAMICAL SYSTEMS NONAUTONOMOUS SETS AND 2-PARAMETER SEMIGROUPS INVARIANT AND LIMIT SETS ATTRACTORS AND GLOBAL ATTRACTORS PERIODIC AND AUTONOMOUS 2-PARAMETER SEMIGROUPS APPLICATIONS: DISCRETIZED SEMI?OWS RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS ABSTRACT EVOLUTION EQUATIONS REACTION-DIFFUSION EQUATIONS DOUBLY NONLINEAR EQUATIONS REMARKS NONAUTONOMOUS DIFFERENCE EQUATIONS BASICS AND EXAMPLES EXISTENCE AND BOUNDEDNESS OF SOLUTIONS DIFFERENCE EQUATIONS AND 2-PARAMETER SEMIGROUPS STABILITY PERIODIC AND AUTONOMOUS DIFFERENCE EQUATIONS APPLICATIONS FULLY DISCRETIZED FUNCTIONAL DIFFERENTIAL EQUATIONS TIME-DISCRETIZED ABSTRACT EVOLUTION EQUATIONS FULLY DISCRETIZED REACTION-DIFFUSION EQUATIONS FULLY DISCRETIZED FINITE DIFFERENCE GINZBURG–LANDAU EQUATION TIME-DISCRETIZED DOUBLY NONLINEAR EQUATIONS LINEAR DIFFERENCE EQUATIONS BASICS PERIODIC LINEAR EQUATIONS INVARIANT SPLITTINGS AND EXPONENTIAL GROWTH DICHOTOMIES AND SPLITTINGS ADMISSIBILITY ROUGHNESS DISCRETIZED LINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS TIME-DISCRETIZED LINEAR ABSTRACT EVOLUTION EQUATIONS TIME-DISCRETIZED LINEAR PARABOLIC EQUATIONS FULLY DISCRETIZED DIFFUSION EQUATIONS INVARIANT FIBER BUNDLES SEMILINEAR DIFFERENCE EQUATIONS EXISTENCE OF INVARIANT FIBER BUNDLES INVARIANT FOLIATIONS AND ASYMPTOTIC PHASE SMOOTHNESS OF FIBER BUNDLES AND FOLIATIONS NORMAL HYPERBOLICITY PSEUDO-STABLE AND PSEUDO-UNSTABLE FIBER BUNDLES INERTIAL FIBER BUNDLES APPROXIMATION OF INVARIANT FIBER BUNDLES DISCRETIZED FUNCTIONAL DIFFERENTIAL EQUATIONS TIME-DISCRETIZED PARABOLIC EVOLUTION EQUATIONS LINEARIZATION TOPOLOGICAL CONJUGATION AND DECOUPLING GENERALIZED HARTMAN–GROBMAN THEOREM SOLUTION CONJUGATION