5 papers · 1 filter
An Index Theorem in Relative K-Theory for First-Order Systems
Robert Skiba, Daniel Strzelecki, Nils Waterstraat
Motivated by bifurcation of branches of homoclinic orbits of dynamical systems, we consider families of first-order equations on the real line and introduce a generalisation of pre…
Evans function, parity and nonautonomous bifurcations
Christian Pötzsche, Robert Skiba
The concept of parity due to Fitzpatrick, Pejsachowicz and Rabier is a central tool in the abstract bifurcation theory of nonlinear Fredholm operators. In this paper, we relate the…
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…
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…