Related papers: Distributionally chaotic $C_0$-semigroups on compl…
We consider two $C_0$-semigroups on function spaces or, more generally, Banach lattices and give necessary and sufficient conditions for the orbits of the first semigroup to dominate the orbits of the second semigroup for large times. As an…
This paper is based on three hours of lectures given by the first author in the "Focus Program on Analytic Function Spaces and their Applications" July 1 -- December 31, 2021, organized by the Fields Institute for Research in Mathematical…
A chaos-based communication scheme allowing simultaneous bidirectional message transmission (Opt. Lett. 32, 403, 2007) is investigated numerically. Incoherent feedback and coupling case is analyzed, which is expected in real long-distance…
The subject of this study is the long-time equilibration dynamics of a strongly disordered one-dimensional chain of coupled weakly anharmonic classical oscillators. It is argued that chaos in this system has a very particular spatial…
A set of bounded linear operators from a Banach space to a Banach lattice is collectively L-weakly compact whenever union of images of the unit ball is L-weakly compact. We extend the Meyer-Nieberg duality theorem to collectively L-weakly…
A model of nonlinear resonance as a periodically perturbed pendulum is considered, and a new method of analytical estimating the width of a chaotic layer near the separatrices of the resonance is derived for the case of slow perturbation…
The statistics of gaps between quantum energy levels is a hallmark criterion in quantum chaos and quantum integrability studies. The relevant distributions corresponding to exactly integrable vs. fully chaotic systems are universal and…
The outskirts of galaxy clusters present a promising avenue for constraining cluster masses in a way that is robust to the impact of baryonic physics. We assess the accuracy to which the cluster infall regions can be used to for cluster…
In the present work we study the concepts of shadowing and chain recurrence in the setting of linear dynamics. We prove that shadowing and finite shadowing always coincide for operators on Banach spaces, but we exhibit operators on the…
Chaotic dynamics can be quite heterogeneous in the sense that in some regions the dynamics are unstable in more directions than in other regions. When trajectories wander between these regions, the dynamics is complicated. We say a chaotic…
We use the method of atomic decomposition and a new family of Banach spaces to study the action of transfer operators associated to piecewise-defined maps. It turns out that these transfer operators are quasi-compact even when the…
We study a control system resembling a singularly perturbed system whose variables are decomposed into groups that change their values with rates of different orders of magnitude. We establish that the slow trajectories of this system are…
We review application of level dynamics to spectra of quantally chaotic systems. We show that statistical mechanics approach gives us predictions about level statistics intermediate between integrable and chaotic dynamics. Then we discuss…
Given a linear closed but not necessarily densely defined operator $A$ on a Banach space $E$ with nonempty resolvent set and a multivalued map $F\colon I\times E\map E$ with weakly sequentially closed graph, we consider the…
We consider a symmetrical star-shaped network, in which bandwidth is shared among the active connections according to the "min" policy. Starting from a chaos propagation hypothesis, valid when the system is large enough, one can write…
Let $A$ be a dissipative operator on a Banach space with a dense domain. It is proved that $A$ has a quasi-dissipative extension (possibly in an enlarged Banach space) which generates a quasi-contractive $C_0$-semigroup. \par This gives a…
Wavefunctions in chaotic and disordered quantum billiards are studied experimentally using thin microwave cavities. The chaotic wavefunctions display universal density distributions and density auto-correlations in agreement with…
An algebra A of operators on a Banach space X is called strictly semi-transitive if for all non-zero x,y in X there exists an operator S in A such that Sx=y or Sy=x. We show that if A is norm-closed and strictly semi-transitive, then every…
This paper focus on investigating the explicit rate of convergence for the propagation of chaos, in a pathwise sense a family of interacting stochastic particle related to some Brownian driven McKean-Vlasov dynamics. Precisely the McKean…
Let S be a dense sub-semigroup of the positive real numbers, and let X be a separable, reflexive Banach space. This note contains a proof that every weakly continuous contractive semigroup of operators on X over S can be extended to a…