22 citations · 65 across the 30 of their papers we have counts for
39 papers
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…
A Comparison Principle for Bifurcation of Periodic Solutions of Hamiltonian Systems
Helene Cyris, Joanna Janczewska, Nils Waterstraat
We obtain novel criteria for the existence of local bifurcation for periodic solutions of Hamiltonian systems by a comparison principle of the spectral flow. Our method allows to f…
On the Uniqueness of the -Equivariant Spectral Flow
Marek Izydorek, Joanna Janczewska, Maciej Starostka +1
The spectral flow is an integer-valued homotopy invariant for paths of selfadjoint Fredholm operators. Lesch as well as Pejsachowicz, Fitzpatrick and Ciriza independently showed th…
Local and Global Bifurcation for Periodic Solutions of Hamiltonian Systems via Comparison Theory for the Spectral Flow
Joanna Janczewska, Maciej Starostka, Nils Waterstraat
We obtain local and global bifurcation for periodic solutions of Hamiltonian systems by using a new way to apply a comparison principle of the spectral flow that was originally int…
Bifurcation for a Class of Indefinite Elliptic Systems by Comparison Theory for the Spectral Flow via an Index Theorem
J. Janczewska, M. Möckel, N. Waterstraat
We consider families of strongly indefinite systems of elliptic PDE and investigate bifurcation from a trivial branch of solutions by using the spectral flow. The novelty in our ap…
The Equivariant Spectral Flow and Bifurcation for Functionals with Symmetries -- Part I
Marek Izydorek, Joanna Janczewska, Maciej Starostka +1
We consider bifurcation of critical points from a trivial branch for families of functionals that are invariant under the orthogonal action of a compact Lie group. Based on a recen…
The relative cup-length in local Morse cohomology
Thomas O. Rot, Maciej Starostka, Nils Waterstraat
Local Morse cohomology associates cohomology groups to isolating neighborhoods of gradient flows of Morse functions on (generally non-compact) Riemannian manifolds . We show tha…
The Equivariant Spectral Flow and Bifurcation of Periodic Solutions of Hamiltonian Systems
Marek Izydorek, Joanna Janczewska, Nils Waterstraat
We define a spectral flow for paths of selfadjoint Fredholm operators that are equivariant under the orthogonal action of a compact Lie group as an element of the representation ri…
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…
On a Comparison Principle and the Uniqueness of Spectral Flow
Maciej Starostka, Nils Waterstraat
The spectral flow is a well-known quantity in spectral theory that measures the variation of spectra about along paths of selfadjoint Fredholm operators. The aim of this work i…
Parity flow as -valued spectral flow
Nora Doll, Hermann Schulz-Baldes, Nils Waterstraat
This note is about the topology of the path space of linear Fredholm operators on a real Hilbert space. Fitzpatrick and Pejsachowicz introduced the parity of such a path, based on…
On the existence of homoclinic type solutions of a class of inhomogenous second order Hamiltonian systems
Jakub Ciesielski, Joanna Janczewska, Nils Waterstraat
We show the existence of homoclinic type solutions of second order Hamiltonian systems with a potential satisfying a relaxed superquadratic growth condition and a forcing term that…
The Maslov Index and the Spectral Flow - revisited
Marek Izydorek, Joanna Janczewska, Nils Waterstraat
We give an elementary proof of a celebrated theorem of Cappell, Lee and Miller which relates the Maslov index of a pair of paths of Lagrangian subspaces to the spectral flow of an…
On the Fredholm Lagrangian Grassmannian, Spectral Flow and ODEs in Hilbert Spaces
Nils Waterstraat
We consider homoclinic solutions for Hamiltonian systems in symplectic Hilbert spaces and generalise spectral flow formulas that were proved by Pejsachowicz and the author in finit…
The -cohomological Conley Index, Cup-Lengths and the Arnold Conjecture on
Maciej Starostka, Nils Waterstraat
We give a new proof of the strong Arnold conjecture for -periodic solutions of Hamiltonian systems on tori, that was first shown by C. Conley and E. Zehnder in 1983. Our proof u…
Not every conjugate point of a semi-Riemannian geodesic is a bifurcation point
Giacomo Marchesi, Alessandro Portaluri, Nils Waterstraat
We revisit an example of a semi-Riemannian geodesic that was discussed by Musso, Pejsachowicz and Portaluri in 2007 to show that not every conjugate point is a bifurcation point. W…
On the existence of homoclinic type solutions of inhomogenous Lagrangian systems
Jakub Ciesielski, Joanna Janczewska, Nils Waterstraat
We study the existence of homoclinic type solutions for second order Lagrangian systems of the type , where , $q\in\mathbb…
Bifurcation of equilibrium forms of an elastic rod on a two-parameter Winkler foundation
Marek Izydorek, Joanna Janczewska, Nils Waterstraat +1
We consider two-parameter bifurcation of equilibrium states of an elastic rod on a deformable foundation. Our main theorem shows that bifurcation occurs if and only if the lineariz…
The Index Bundle and Multiparameter Bifurcation for Discrete Dynamical Systems
Robert Skiba, Nils Waterstraat
We develop a -theoretic approach to multiparameter bifurcation theory of homoclinic solutions of discrete non-autonomous dynamical systems from a branch of stationary solutions.…
A K-theoretical Invariant and Bifurcation for Homoclinics of Hamiltonian Systems
Alessandro Portaluri, Nils Waterstraat
We revisit a K-theoretical invariant that was invented by the first author some years ago for studying multiparameter bifurcation of branches of critical points of functionals. Our…
A Remark on Bifurcation of Fredholm Maps
Nils Waterstraat
We modify an argument for multiparameter bifurcation of Fredholm maps by Fitzpatrick and Pejsachowicz to strengthen results on the topology of the bifurcation set. Furthermore, we…
Fredholm Operators and Spectral Flow
Nils Waterstraat
These are extended lecture notes of a PhD course that the author gave at the Universita degli studi di Torino in Italy in spring 2013.
Spectral flow and bifurcation for a class of strongly indefinite elliptic systems
Nils Waterstraat
We consider bifurcation of solutions from a given trivial branch for a class of strongly indefinite elliptic systems via the spectral flow. Our main results establish bifurcation i…