Lecture Notes in Mathematics

On the measure-preserving flow on the torus.- Breaking of waves.- Group extensions of discrete dynamical systems.- Conditions for integrability of certain equations.- Formalisme Lagrangien.- Continuous flows on the plane.- Non-linear cubic differential equations.- Mathematical theory of general systems.- Mathematical theory of multi-level systems.- Geometric elements in the theory of transformations of ordinary second-order linear differential equations.- Dynamical systems on an n-torus.- Continuous flows on the plane : techniques I.- Continuous flows on the plane : techniques II.- Generalisation of Bendixson's theory.- Geodesic flows.- Instability.- One-parameter families of diffeomorphisms.- Topology and mechanics.- Generic properties of conservative systems.- Dynamical systems on nilmanifolds.- Linearizing a diffeomorphism.- Topologically transitive diffeomorphisms of T4.- ?-explosions.- Singularities of exponential maps.- Periodic points, measures and Axiom A.- Holomorphic vector fields on CP2.- Small delays don't matter.- Conjugacy and ergodicity.- SL(n,R) actions.- Diff(M) is simple?.- Distributed parameters control.- Flows outside a compact invariant set.- Non-linear Volterra equations.- Ergodic Hamiltonian theory.- Subharmonic solutions to Duffing's equation.- Similarity of automorphisms of the torus.- Differential equations with periodic coefficients.- An algebraic approach to dynamical systems.- Volterra equations and semi-flows.- Homomorphisms of minimal sets.- Boundedness of solutions of 2nd order equations.- Mobius transformations in stability theory.- Some maximum principles for Ito equations.- A periodic wave propagation model for pattern formation in embryos.- Intrinsically ergodic systems.- The group of diffeomorphisms, and motion of fluids.- Positional information and the spatial pattern of cellular differentiation.- Bifurcations.- Theorie de Fuchs sur une variete analytique complexe.- Invariant subsets of hyperbolic sets.- The principle of Maupertuis.- Instability in Diffr(T3).- A global concept of stability under persistent perturbations.- Hausdorff dimension and transversality of discrete flows.- Universal foliations.- Foliations of the plane.- Synthesis of control systems on manifolds.- Foliations and transformation groups.- Report on Bott's theorem on foliations.- Topological equivalence of foliations.- Foliations.- Diffeomorphismes du tore T3.- Foliations.- Algebraic invariants of foliations.- Work of gromov: generalization of the Smale-Hirsch theorem.- List of speakers at the afternoon sessions of the summer school 15th - 25th July 1969.- Foliations of codimension one.- Expanding attractors.- Equivalence of dynamical systems.- Generic bifurcation.- Probabilistic convergence of approximations for partial differential equations.- Mathematical structure of network synthesis.- Actions of R2 on manifolds.- A generalization of Mackey's imprimitivity theorem.- Algebraic problems in dynamical systems.- Almost periodic minimal sets.- Anosov diffeomorphisms.- Sufficiency of jets.- Asymmetric manifolds (Report withdrawn).- Universal unfoldings (Report not received).- Functional-differential systems and pattern learning.- Stability theory for partial differential equations.- A functional approach to stability of differential equations.- Numerical analysis of nonlinear oscillations.- Dichotomies and stability theory.- Commuting diffeomorphisms.- Predictions for the future of differential equations.- For Ralph.