Related papers: Globally stable cylinders for hyperbolic CAT(0) cu…
We prove moduli spaces of semistable parabolic bundles and generalized parabolic sheaves with fixed determinant on a smooth projective curve are globally $F$-regular type.
This paper studies a fundamental relation that exists between stabilizability assumptions usually employed in distributed model predictive control implementations, and the corresponding notions of invariance implicit in such controllers.…
The stability problem of a class of nonlinear switched systems defined on compact sets with state-dependent switching is considered. Instead of the Caratheodory solutions, the general Filippov solutions are studied. This encapsulates…
We examine Hilbert-Schmidt stability (HS-stability) of discrete amenable groups from several angles. We give a short, elementary proof that finitely generated nilpotent groups are HS-stable. We investigate the permanence of HS-stability…
This paper presents a deterministic hybrid observer for the attitude dynamics of a rigid body that guarantees global asymptotical stability. Any smooth attitude observer suffers from the inherent topological restriction that it is…
We examine positive and negative results for the Gromov-Lawson-Rosenberg Conjecture within the class of crystallographic groups. We give necessary conditions within the class of split extensions of free abelian by cyclic groups to satisfy…
We report conditions on a switching signal that guarantee that solutions of a switched linear systems converge asymptotically to zero. These conditions are apply to continuous, discrete-time and hybrid switched linear systems, both those…
We prove that each \omega-categorical, generically stable group is solvable-by-finite.
In this paper it is shown that every finite cyclic group satisfies the CI-property for the class of balanced configurations.
We introduce a new kind of action of a relatively hyperbolic group on a CAT(0) cube complex, called a relatively geometric action. We provide an application to characterize finite-volume Kleinian groups in terms of action on cube complexes,…
A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be…
We prove two results about generically stable types $p$ in arbitrary theories. The first, on existence of strong germs, generalizes results from D. Haskell, E. Hrushovski and D. Macpherson on stably dominated types. The second is an…
For a nearly integrable Hamiltonian systems $H=h(p)+\epsilon P(p,q)$ with $(p,q)\in\mathbb{R}^3\times\mathbb{T}^3$, large normally hyperbolic invariant cylinders exist along the whole resonant path, except for the…
A hyperbolic group acts by homeomorphisms on its Gromov boundary. We use a dynamical coding of boundary points to show that such actions are topologically stable in the dynamical sense: any nearby action is semi-conjugate to (and an…
We show that a finitely generated subgroup of the genus two handlebody group is stable if and only if the orbit map to the disk graph is a quasi-isometric embedding. To this end, we prove that the genus two handlebody group is a…
In this paper we show how the existence of a certain stable cylinder determines (locally) the ambient manifold where it is immersed. This cylinder has to verify a {\it bifurcation phenomena}, we make this explicit in the introduction. In…
A group may be considered $C^*$-stable if almost representations of the group in a $C^*$-algebra are always close to actual representations. We initiate a systematic study of which discrete groups are $C^*$-stable or only stable with…
In this paper we prove a closure result for globally hyperbolic spacetimes satisfying, at a certain time, natural assumptions on the deceleration, the pressure and the Hubble constant. The main tool that we use is a general Bonnet-Myers…
This paper is devoted to the generic transversality of radially symmetric stationary solutions of nonlinear parabolic systems of the form \[ \partial_t w(x,t) = -\nabla V\bigl(w((x,t))\bigr) + \Delta_x w(x,t) \,, \] where the space variable…
Let $H$ be an acylindrically hyperbolic group without nontrivial finite normal subgroups. We show that any finite system $S$ of equations with constants from $H$ is equivalent to a single equation. We also show that the algebraic set…