Related papers: On the stable Conley index in Hilbert spaces
In this paper we connect algebraic properties of the pair-of-pants product in local Floer homology and Hamiltonian dynamics. We show that for an isolated periodic orbit the product is non-uniformly nilpotent and use this fact to give a…
We introduce a method to reconstruct an element of a Hilbert space in terms of an arbitrary finite collection of linearly independent reconstruction vectors, given a finite number of its samples with respect to any Riesz basis. As we…
By considering labeled configurations of ``bounded multiplicity'', one can construct a functor that fits between homology and stable homotopy. Based on previous work, we are able to give an equivalent description of this labeled…
In this sequence, we first prove an abstract Morse index theorem in a Hilbert space modeling a variational problem with constraints. Then, our abstract formulation is applied to study several optimization setups including closed CMC…
We investigate stability of both localized time-periodic coherent states (pulsons) and uniformly distributed coherent states (oscillating condensate) of a real scalar field satisfying the Klein-Gordon equation with a logarithmic…
We study statistical inference on unit roots and cointegration for time series in a Hilbert space. We develop statistical inference on the number of common stochastic trends embedded in the time series, i.e., the dimension of the…
We compute the stable cohomology of moduli spaces of hyperelliptic curves of a fixed genus embedded on a fixed Hirzebruch surface. We also describe these moduli spaces of embedded hyperelliptic curves in terms of moduli spaces of pointed…
Combinatorial vector fields on simplicial complexes as introduced by Robin Forman have found numerous and varied applications in recent years. Yet, their relationship to classical dynamical systems has been less clear. In recent work it was…
We incorporate pearly Floer trajectories into the transversality scheme for pseudoholomorphic maps introduced by Cieliebak-Mohnke. By choosing generic domain-dependent almost complex structures we obtain zero and one-dimensional moduli…
We provide a simplified approach to the the stable Hopf invariant. We provide short elementary proofs of the Cartan Formula, the Composition Formula, and the Transfer formula. In addition, when $\pi$ is a discrete group, we show how to…
We establish a Sharkovskii-type theorem for a class of discrete random dynamical systems via the random Conley index. Using the continuation property of the Conley index, we extend classical forcing results to random systems obtained from…
We study the model theory of expansions of Hilbert spaces by generic predicates. We first prove the existence of model companions for generic expansions of Hilbert spaces in the form first of a distance function to a random substructure,…
We investigate convergence properties of discrete-time semigroup quantum dynamics, including asymptotic stability, probability and speed of convergence to pure states and subspaces. These properties are of interest in both the analysis of…
We extend the Cohen-Jones-Segal construction of stable homotopy types associated to flow categories of Morse-Smale functions $f$ to the setting where $f$ is equivariant under a finite group action and is Morse but no longer Morse-Smale.…
We introduce sparse versions of function spaces that are relevant to characterize the solutions of Euler equations without concentration. The standard Sobolev space $H^{-1}$ is given a sparse structure that allows to measure the degree of…
We study a wide class of topological free-fermion systems on a hypercubic lattice in spatial dimensions $d\ge 1$. When the Fermi level lies in a spectral gap or a mobility gap, the topological properties, e.g., the integral quantization of…
We observe that a simple condition suffices to describes non-forking independence over models in a stable theory. Under mild assumptions, this description can be extended to non-forking independence over algebraically closed subsets,…
We study cocycles of compact operators acting on a separable Hilbert space, and investigate the stability of the Lyapunov exponents and Oseledets spaces when the operators are subjected to additive Gaussian noise. We show that as the noise…
We consider an $\alpha$-relaxed projection $P_A^\alpha:H\to H$ given by $P_A^\alpha(x)=\alpha P_A(x)+(1-\alpha)x$ where $\alpha\in[0,1]$ and $P_A$ is the projection onto a non-empty, convex and closed subset $A$ of the real Hilbert space…
Conley in \cite{Con} constructed a complete Lyapunov function for a flow on compact metric space which is constant on orbits in the chain recurrent set and is strictly decreasing on orbits outside the chain recurrent set. This indicates…