Related papers: Global dynamics of contact Hamiltonian systems (I)…
Hamiltonian dynamics describing conservative systems naturally preserves the standard notion of phase-space volume, a result known as the Liouville's theorem which is central to the formulation of classical statistical mechanics. In this…
Previous results have shown that a large class of complex systems consisting of many interacting heterogeneous phase oscillators exhibit an attracting invariant manifold. This result has enabled reduced analytic system descriptions from…
This paper studies the behavior of dynamical systems in non-compact spaces, specifically focusing on the concepts of global attractors and shadowing. Let $K$ be a compact global attractor. We show that the shadowing property holds in…
The evolution of a system of chemical reactions can be studied, in the eikonal approximation, by means of a Hamiltonian dynamical system. The fixed points of this dynamical system represent the different states in which the chemical system…
We study Hamiltonian flows in a real separable Hilbert space endowed with a symplectic structure. Measures on the Hilbert space that are invariant with respect to the flows of completely integrable Hamiltonian systems are investigated.…
We provide new insights into the contact Hamiltonian and Lagrangian formulations of dissipative mechanical systems. In particular, we state a new form of the contact dynamical equations, and we review two recently presented Lagrangian…
Two types of dynamics, chaotic and monotone, are compared. It is shown that monotone maps in strongly ordered spaces do not have chaotic attracting sets.
This paper investigates the complex nonlinear dynamics of an optomechanical system featuring an optical cavity coupled to two mechanical resonators interconnected by a phase-dependent interaction. We specifically explore the role of this…
We consider $k$-dimensional discrete-time systems of the form $x_{n+1}=F(x_n,\ldots,x_{n-k+1})$ in which the map $F$ is continuous and monotonic in each one of its arguments. We define a partial order on $\mathbb{R}^{2k}_+$, compatible with…
This paper is devoted to a long time behavior analysis associated with flow structure interactions at subsonic and supersonic velocities. It turns out that an ntrinsic component of that analysis is the study of attracting sets corresponding…
In this work, we perform a careful study of an special arrangement of coupled systems that consists of two external harmonic oscillators weakly coupled to an arbitrary network (data bus) of strongly interacting oscillators. Our aim is to…
In many complex systems, states and interaction structure coevolve towards a dynamic equilibrium. For the adaptive contact process, we obtain approximate expressions for the degree distributions that characterize the interaction network in…
Differential geometric structures such as the principal bundle for the canonical vector bundle on a complex Grassmann manifold, the canonical connection form on this bundle, the canonical symplectic form on a complex Grassmann manifold and…
The paper is devoted to the dynamics of dissipative gap solitons in the periodically corrugated optical waveguides whose spectrum of linear excitations contains a mode that can be referred to as a quasi-Bound State in the Continuum. These…
We discuss recent results obtained for the Hamiltonian Mean Field model. The model describes a system of N fully-coupled particles in one dimension and shows a second-order phase transition from a clustered phase to a homogeneous one when…
The constants of motion of the following systems are deduced: a relativistic particle with linear dissipation, a no-relativistic particle with a time explicitly depending force, a no-relativistic particle with a constant force and time…
A discrete dynamical system in Euclidean m-space generated by the iterates of an asymptotically zero map f, satisfying f(x) goes to zero as x goes to infinity, must have a compact global attracting set $A $. The question of what additional…
Higher-order topological crystalline phases in low-dimensional interacting quantum systems represent a challenging and largely unexplored research topic. Here, we derive a Hamiltonian describing fermions interacting through correlated…
A one-dimensional bosonic gas with strong contact repulsion and attractive non-local interactions may form a quantum droplet with a flat-top density profile. We focus on a system in the Tonks-Girardeau limit of infinitely strong contact…
The past few years have seen many advances in our understanding of the dynamics of polymeric fluids. These include improvements on the successful reptation theory; an emerging molecular theory of semiflexible chain dynamics; and an…