Zobrazeno 1 - 10
of 411
pro vyhledávání: '"Waterstraat A"'
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 approach is a refined version of a comparison principle that was origina
Externí odkaz:
http://arxiv.org/abs/2405.19473
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
Autor:
Meißner-Bendzko, Nico, Waterstraat, Gunnar, Curio, Gabriel, Rocco, Andrea, Hofmann-Shen, Christina
Publikováno v:
In Clinical Neurophysiology November 2024 167:254-261
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
Publikováno v:
Frontiers in Bioengineering and Biotechnology, Vol 12 (2024)
Shunt surgery is the main treatment modality for hydrocephalus, the leading cause of brain surgery in children. The efficacy of shunt surgery, particularly in infant hydrocephalus, continues to present serious challenges in achieving improved outcome
Externí odkaz:
https://doaj.org/article/1744d9b6cfb54e5dad86347ab2f8d48b
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
Akademický článek
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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