Generalized Cohomological Index Theories for Lie Group Actions with an Application to Bifurcation Questions for Hamiltonian Systems.
Generalized Hopf bifurcations and applications to planar quadratic systems
Generic bifurcation of reversible vector fields on a 2-bidimensional manifold.
In this paper we deal with reversible vector fields on a 2-dimensional manifold having a codimension one submanifold as its symmetry axis. We classify generically the one parameter families of such vector fields. As a matter of fact, aspects of structural stability and codimension one bifurcation are analysed.
Generic Bifurcations of Varieties.
Generic robustness of spectral decompositions
Generic saddle-node bifurcation for cascade second order ODEs on manifolds
Cascade second order ODEs on manifolds are defined. These objects are locally represented by coupled second order ODEs such that any solution of one of them can represent an external force for the other one. A generic saddle-node bifurcation theorem for 1-parameter families of cascade second order ODEs is proved.
Geodesics on S2 and periodic points of annulus homeomorphisms.
Global attractor of a differentiable autonomous system on the plane
We study the structure of a differentiable autonomous system on the plane with non-positive divergence outside a bounded set. It is shown that under certain conditions such a system has a global attractor. The main result here can be seen as an improvement of the results of Olech and Meisters in [7,9] concerning the global asymptotic stability conjecture of Markus and Yamabe and the Jacobian Conjecture.
Global behavior of four competitive rational systems of difference equations in the plane.
Global bifurcation from the Fučik spectrum
Global bifurcation of homoclinic trajectories of discrete dynamical systems
We prove the existence of an unbounded connected branch of nontrivial homoclinic trajectories of a family of discrete nonautonomous asymptotically hyperbolic systems parametrized by a circle under assumptions involving topological properties of the asymptotic stable bundles.
Global bifurcation result for the -biharmonic operator.
Global Existence of Periodic Solutions in a Delayed Tumor-Immune Model
This paper is devoted to the study of global existence of periodic solutions of a delayed tumor-immune competition model. Also some numerical simulations are given to illustrate the theoretical results
Global stability of saddle-node bifurcation of a periodic orbit for vector fields
Group analysis methods for construction and investigation of the bifurcation equation
Heteroclinic cycles emanating from local bifurcations.
Heteroclinic solutions for perturbed second order systems
The existence of infinitely many heteroclinic orbits implying a chaotic dynamics is proved for a class of perturbed second order Lagrangian systems possessing at least 2 hyperbolic equilibria.
Heterodimensional cycles, partial hyperbolicity and limit dynamics
We study one-parameter families of diffeomorphisms unfolding heterodimensional cycles (i.e. cycles containing periodic points of different indices). We construct an open set of such arcs such that, for a subset of the parameter space with positive relative density at the bifurcation value, the resulting nonwandering set is the disjoint union of two hyperbolic basic sets of different indices and a strong partially hyperbolic set which is robustly transitive. The dynamics of the diffeomorphisms we...
Higher order branching of periodic orbits from polynomial isochrones.
Higher order Poincaré-Pontryagin functions and iterated path integrals