5 papers
Global bifurcation of homoclinic solutions
Iacopo P. Longo, Christian Pötzsche, Robert Skiba
In the analysis of parametrized nonautonomous evolutionary equations, bounded entire solutions are natural candidates for bifurcating objects. Appropriate explicit and sufficient c…
The Index Bundle for Selfadjoint Fredholm Operators and Multiparameter Bifurcation for Hamiltonian Systems
Robert Skiba, Nils Waterstraat
The index of a selfadjoint Fredholm operator is zero by the well-known fact that the kernel of a selfadjoint operator is perpendicular to its range. The Fredholm index was generali…
Fredholm theory of families of discrete dynamical systems and its applications to bifurcation theory
Robert Skiba, Nils Waterstraat
In a previous work, we proved an index theorem for families of asymptotically hyperbolic discrete dynamical systems and obtained applications to bifurcation theory. A weaker and fa…
Global continuation of homoclinic solutions
Christian Potzsche, Robert Skiba
When extending bifurcation theory of dynamical systems to nonautonomous problems, it is a central observation that hyperbolic equilibria persist as bounded entire solutions under s…
Global bifurcation of homoclinic trajectories of discrete dynamical systems
Jacobo Pejsachowicz, Robert Skiba
We prove the existence of an unbounded connected branch of nontrivial homoclinic trajectories of a family of discrete nonautonomous asymptotically hyperbolic systems parametrized b…