Dynamical Systems and Turbulence, Warwick 1980

Inhaltsverzeichnis

• Lectures on bifurcation from periodic orbits.
• General introduction to steady state bifurcation.
• Anosov diffeomorphisms with pinched spectrum.
• Formal normal form theorems for vector fields and some consequences for bifurcations in the volume preserving case.
• Quasi periodic flow near a codimension one singularity of a divergence free vector field in dimension three.
• A C2 Kupka-Smale diffeomorphism of the disk with no sources or sinks.
• On a codimension two bifurcation.
• Stability and bifurcation in a parabolic equation.
• Wandering intervals.
• Space- and time-periodic perturbations of the Sine-Gordon equation.
• Simple computation of bifurcating invariant circles for mappings.
• Families of vector fields with finite modulus of stability.
• On the dimension of the compact invariant sets of certain non-linear maps.
• More topological entropy for geodesic flows.
• Controllability of multi-trajectories on Lie groups.
• Characterising diffeomorphisms with modulus of stability one.
• Algebraic Kupka-Smale theory.
• Differentiability of the stable foliation for the model Lorenz equations.
• On the bifurcations creating horseshoes.
• Saddle connections of arcs of diffeomorphisms: Moduli of stability.
• Detecting strange attractors in turbulence.
• Local and simultaneous structural stability of certain diffeomorphisms.