Zobrazeno 1 - 10
of 126
pro vyhledávání: '"Waterstraat, Nils"'
This is the first treatment entirely dedicated to an analytic study of spectral flow for paths of selfadjoint Fredholm operators, possibly unbounded or understood in a semi finite sense. The importance of spectral flow for homotopy and index theory a
Externí odkaz:
https://library.oapen.org/handle/20.500.12657/63798
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 recent construction of an equivariant spectral flow by the authors, we obta
Externí odkaz:
http://arxiv.org/abs/2306.01170
Local Morse cohomology associates cohomology groups to isolating neighborhoods of gradient flows of Morse functions on (generally non-compact) Riemannian manifolds $M$. We show that local Morse cohomology is a module over the cohomology of the isolat
Externí odkaz:
http://arxiv.org/abs/2212.10309
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 ring of the latter. This $G$-equivariant spectral flow shares all common
Externí odkaz:
http://arxiv.org/abs/2104.01586
Autor:
Skiba, Robert, Waterstraat, Nils
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 generalised to families by Atiyah and J\"anich in the sixties, and it is readi
Externí odkaz:
http://arxiv.org/abs/2012.05691
Fredholm theory of families of discrete dynamical systems and its applications to bifurcation theory
Autor:
Skiba, Robert, Waterstraat, Nils
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 far more common assumption than asymptotic hyperbolicity is the existenc
Externí odkaz:
http://arxiv.org/abs/2003.12433
Autor:
Starostka, Maciej, Waterstraat, Nils
The spectral flow is a well-known quantity in spectral theory that measures the variation of spectra about $0$ along paths of selfadjoint Fredholm operators. The aim of this work is twofold. Firstly, we consider homotopy invariance properties of the
Externí odkaz:
http://arxiv.org/abs/1910.05183
Akademický článek
Tento výsledek nelze pro nepřihlášené uživatele zobrazit.
K zobrazení výsledku je třeba se přihlásit.
K zobrazení výsledku je třeba se přihlásit.
Publikováno v:
Bulletin of the London Mathematical Society 51, 836-852, 2019
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 the Leray-Schauder degree of a path of parametrices. Here an alternati
Externí odkaz:
http://arxiv.org/abs/1812.07780
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 is sufficiently small in the space of square integrable functions. Th
Externí odkaz:
http://arxiv.org/abs/1810.03021