The Bifurcation Set and Logarithmic Vector Fields.
The Birkhoff-Lewis Fixed Point Theorem and a Conjecture of V.I. Arnold.
The compact category and mulitple periodic solutions of Hamiltionian systems on symmetric starshaped energy surfaces.
The Conley index over a space.
The explosion of singular cycles
The index of a vector field tangent to a hypersurface and the signature of the relative jacobian determinant
Given a real analytic vector field tangent to a hypersurface with an algebraically isolated singularity we introduce a relative Jacobian determinant in the finite dimensional algebra associated with the singularity of the vector field on . We show that the relative Jacobian generates a 1-dimensional non-zero minimal ideal. With its help we introduce a non-degenerate bilinear pairing, and its signature measures the size of this point with sign. The signature satisfies a law of conservation of...
The number of buckled states of circular plates
The Rotating String.
The unfoldings of a germ of vector fields in the plane with a singularity of codimension 3
The Weinstein conjecture in cotangent bundles and related results
There are Two Isotopic Morse-Smale Diffeomorphisms Which Cannot be Joined by Simple Arcs.
Topological Classification and Bifurcations of Holomorphic Flows with Resonances in ...2.