Tangencies for real and complex Hénon maps: An analytic method.
The existence of homoclinic solutions for hyperbolic equations.
The period function near a polycycle with two semi-hyperbolic vertices
The shadowing chain lemma for singular Hamiltonian systems involving strong forces
We consider a planar autonomous Hamiltonian system :q+∇V(q) = 0, where the potential V: ℝ2 {ζ→ ℝ has a single well of infinite depth at some point ζ and a strict global maximum 0at two distinct points a and b. Under a strong force condition around the singularity ζ we will prove a lemma on the existence and multiplicity of heteroclinic and homoclinic orbits - the shadowing chain lemma - via minimization of action integrals and using simple geometrical arguments.
Transversal homoclinics in nonlinear systems of ordinary differential equations.
Traveling wave fronts in spatially discrete reaction-diffusion equations on higher-dimensional lattices.
Travelling wave solutions for the Painlevé-integrable coupled KdV equations.