Related papers: Contraction Theory for Dynamical Systems on Hilber…
We develop a contraction-based framework to establish the existence and exponential stability of periodic solutions in planar nonsmooth dynamical systems governed by Filippov differential inclusions. The method integrates a time- and…
The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with…
This paper investigates first-order variable metric backward forward dynamical systems associated with monotone inclusion and convex minimization problems in real Hilbert space. The operators are chosen so that the backward-forward…
The design of fixed point algorithms is at the heart of monotone operator theory, convex analysis, and of many modern optimization problems arising in machine learning and control. This tutorial reviews recent advances in understanding the…
This paper is motivated by the problem of quantitatively bounding the convergence of adaptive control methods for stochastic systems to a stationary distribution. Such bounds are useful for analyzing statistics of trajectories and…
We consider characterisations of unitary dilations and approximations of irreversible classical dynamical systems on a Hilbert space. In the commutative case, building on the work in [9], one can express well known approximants (e.g. Hille-…
We discuss the two closely related, but different concepts of weak and almost weak stability for the powers of a contraction on a separable Hilbert space. Extending Halmos' and Rohlin's theorems in ergodic theory as a model, we show that…
In this article, we investigate the convergence behavior of two classes of gathering protocols with fixed circulant topologies using tools from dynamical systems. Given a fixed number of mobile entities moving in the Euclidean plane, we…
Relativistic kinematics is usually considered only as a manifestation of pseudo-Euclidean (Lorentzian) geometry of space-time. However, as it is explicitly stated in General Relativity, the geometry itself depends on dynamics, specifically,…
We introduce a discrete dynamical system on the integers, defined by moving a composite $m$ forward to $m+\pi(m)$ and a prime $p$ backward to $p-\mathrm{prevprime}(p)$. This map produces trajectories whose contraction properties are closely…
It is well know that for globally contractive autonomous systems, there exists a unique equilibrium and the distance to the equilibrium evaluated along any trajectory decreases exponentially with time. We show that, additionally, the…
Quantum kinetically constrained models have recently attracted significant attention due to their anomalous dynamics and thermalization. In this work, we introduce a hitherto unexplored family of kinetically constrained models featuring a…
The approach to a substantiation of thermodynamics is offered. A conservative system of interacting elements, which is not in equilibrium, is used as a model. This system is then split into small subsystems that are accepted as being in…
We propose a novel framework for learning stabilizable nonlinear dynamical systems for continuous control tasks in robotics. The key contribution is a control-theoretic regularizer for dynamics fitting rooted in the notion of…
In this work, we leverage the 2-contraction theory, which extends the capabilities of classical contraction theory, to develop a global stability framework. Coupled with powerful geometric tools such as the Poincare index theory, the…
In this paper we prove the following result, useful and often needed in the study of the ergodic properties of hard ball systems: In any such system, for any phase point x with a non-singular forward trajectory and infinitely many connected…
We employ techniques from optimal transport in order to prove decay of transfer operators associated to iterated functions systems and expanding maps, giving rise to a new proof without requiring a Doeblin-Fortet (or Lasota-Yorke)…
A subcritical pattern-forming system with nonlinear advection in a bounded domain is recast as a slow-fast system in space and studied using a combination of geometric singular perturbation theory and numerical continuation. Two types of…
Quantum systems with constraints are often considered in modern theoretical physcics. All realistic field models based on the idea of gauge symmetry are of this type. A partial case of constraints being linear in coordinate and momenta…
It has been recently pointed out that dynamical systems depending on future values of the unknowns may be useful in different areas of knowledge. We explore in this context the extension of the concept of order reduction that has been…