6 papers · 1 filter
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…
Numerical dynamics of integrodifference equations: Periodic solutions and invariant manifolds in
Christian Pötzsche
Integrodifference equations are versatile models in theoretical ecology for the spatial dispersal of species evolving in non-overlapping generations. The dynamics of these infinite…
Urysohn and Hammerstein operators on H"older spaces
Christian Pötzsche
We present an application-oriented approach to Urysohn and Hammerstein integral operators acting between spaces of H"older continuous functions over compact metric spaces. These no…
Numerical Dynamics of Integrodifference Equations: Forward Dynamics and Pullback Attractors
Huy Huynh, Peter E. Kloeden, Christian Pötzsche
In order to determine the dynamics of nonautonomous equations both their forward and pullback behavior need to be understood. For this reason we provide sufficient criteria for the…
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…