Related papers: On infinitesimal contraction analysis for hybrid s…

We introduce the concept of a control contraction metric, extending contraction analysis to constructive nonlinear control design. We derive sufficient conditions for exponential stabilizability of all trajectories of a nonlinear control…

An adequate characterization of the dynamics of Hamiltonian systems at physically relevant scales has been largely lacking. Here we investigate this fundamental problem and we show that the finite-scale Hamiltonian dynamics is governed by…

Synchronization of coupled dynamical systems is a widespread phenomenon in both biological and engineered networks, and understanding this behavior is crucial for controlling such systems. Considerable research has been dedicated to…

We develop a new general algorithm for finding a regular tight-binding lattice Hamiltonian in infinite dimensions for an arbitrary given shape of the density of states (DOS). The availability of such an algorithm is essential for the…

This paper is devoted to the study of symplectic manifolds and their connection with Hamiltonian dynamical systems. We review some properties and operations on these manifolds and see how they intervene when studying the complete…

While compactness is an essential assumption for many results in dynamical systems theory, for many applications the state space is only locally compact. Here we provide a general theory for compactifying such systems, i.e. embedding them…

We provide the detailed asymptotic behavior for first-order aggregation models of heterogeneous oscillators. Due to the dissimilarity of natural frequencies, one could expect that all relative distances converge to definite positive value…

This paper looks to apply the mathematical framework of the Theory of Functional Connections to the solution of boundary-value problems arising from hybrid systems. The Theory of Functional Connections is a technique to derive constrained…

We review in detail the Hamiltonian dynamics for constrained systems. Emphasis is put on the total Hamiltonian system rather than on the extended Hamiltonian system. We provide a systematic analysis of (global and local) symmetries in total…

Equations governing the nonlinear dynamics of complex systems are usually unknown and indirect methods are used to reconstruct their manifolds. In turn, they depend on embedding parameters requiring other methods and long temporal sequences…

This is my dissertation. Its research object is a symmetric group of permutations acting on a finite set. The density of permutations with a given cycle structure pattern is explored when the group order tends to infinity. New and sharper…

The analysis of global dynamics, particularly the identification and characterization of attractors and their regions of attraction, is essential for complex nonlinear and hybrid systems. Combinatorial methods based on Conley's index theory…

In this thesis, it is presented a set of results in adiabatic dynamics (closed and open system) and transitionless quantum driving that promote some advances in our understanding on quantum control and Hamiltonian inverse engineering. In…

Symmetry-informed machine learning can exhibit advantages over machine learning which fails to account for symmetry. In the context of continuous symmetry detection, current state of the art experiments are largely limited to detecting…

The long-term distributions of trajectories of a flow are described by invariant densities, i.e. fixed points of an associated transfer operator. In addition, global slowly mixing structures, such as almost-invariant sets, which partition…

This paper is a survey of extensions to finite automata theory to model real-time systems as well as systems exhibiting mixed discrete-continuous behavior. Real-time systems maintain a continuous and timely interaction with the environment,…

This article is concerned with analytic Hamiltonian dynamical systems in infinite dimension in a neighborhood of an elliptic fixed point. Given a quadratic Hamiltonian, we consider the set of its analytic higher order perturbations. We…

Rigid bodies, plastic impact, persistent contact, Coulomb friction, and massless limbs are ubiquitous simplifications introduced to reduce the complexity of mechanics models despite the obvious physical inaccuracies that each incurs…

The sequential compactness afforded hybrid systems under mild regularity constraints guarantee outer/upper semicontinuous dependence of solutions on initial conditions and perturbations. For reachable sets of hybrid systems, this property…

This paper introduces indefinite proximities inherent in the collection of physical objects found in a dynamical system. Axiomatically, these indefinite proximities lead to a new form of Hausdorff topology, which is indefinite…