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pro vyhledávání: '"Starostka, Maciej"'
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:
Asselle, Luca, Starostka, Maciej
We show that the Hamiltonian action satisfies the Palais-Smale condition over a "mixed regularity" space of loops in cotangent bundles, namely the space of loops with regularity $H^s$, $s\in (\frac 12, 1)$, in the base and $H^{1-s}$ in the fiber dire
Externí odkaz:
http://arxiv.org/abs/2003.10133
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
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Autor:
Starostka, Maciej
We show that there exist two proper gradient vector fields on $\mathbb{R}^n$ which are homotopic in the category of proper maps but not homotopic in the category of proper gradient maps.
Comment: 5 pages
Comment: 5 pages
Externí odkaz:
http://arxiv.org/abs/1809.01411
Autor:
Starostka, Maciej, Waterstraat, Nils
We give a new proof of the strong Arnold conjecture for $1$-periodic solutions of Hamiltonian systems on tori, that was first shown by C. Conley and E. Zehnder in 1983. Our proof uses other methods and is shorter than the previous one. We first show
Externí odkaz:
http://arxiv.org/abs/1708.09631
Autor:
Izydorek, Marek, Rot, Thomas O., Starostka, Maciej, Styborski, Marcin, Vandervorst, Robert C. A. M.
In this paper we introduce a new compactness condition - Property (C) - for flows in (not necessary locally compact) metric spaces. For such flows a Conley type theory can be developed. For example (regular) index pairs always exist for Property-(C)
Externí odkaz:
http://arxiv.org/abs/1612.05524
Autor:
Asselle, Luca, Starostka, Maciej
Publikováno v:
NoDEA: Nonlinear Differential Equations & Applications; Sep2024, Vol. 31 Issue 5, p1-16, 16p
Autor:
Starostka, Maciej
Main theorem of this paper states that Floer cohomology groups in a Hilbert space are isomorphic to the cohomological Conley Index. It is also shown that calculating cohomological Conley Index does not require finite dimensional approximations of the
Externí odkaz:
http://arxiv.org/abs/1401.7811