Related papers: Emerging attractors and the transition from dissip…
The dynamics of the spin-boson Hamiltonian is considered in the stochastic approximation. The Hamiltonian describes a two-level system coupled to an environment and is widely used in physics, chemistry and the theory of quantum measurement.…
We study the dissipative evolution of (0+1)-dimensionally expanding media with Bjorken symmetry using the Boltzmann equation for massive particles in relaxation-time approximation. Breaking conformal symmetry by a mass induces a non-zero…
Power-law sensitivity to initial conditions, characterizing the behaviour of dynamical systems at their critical points (where the standard Liapunov exponent vanishes), is studied in connection with the family of nonlinear 1D logistic-like…
We study the dynamics of the attractor of the doubling map with an asymmetrical hole by associating to each hole an element of the lexicographic world. A description of the topological entropy function is given. We show that the set of…
In this work we use the formalism of chord functions (\emph{i.e.} characteristic functions) to analytically solve quadratic non-autonomous Hamiltonians coupled to a reservoir composed by an infinity set of oscillators, with Gaussian initial…
This paper refined and introduced some notations (namely attractors, physical attractors, proper attractors, topologically exact and topologically mixing) within the context of relations. We establish necessary and sufficient conditions,…
Linear waves in bounded inviscid fluids do not generally form normal modes with regular eigenfunctions. Examples are provided by inertial waves in a rotating fluid contained in a spherical annulus, and internal gravity waves in a stratified…
Chaotic dynamics, commonly seen in weather systems and fluid turbulence, are characterized by their sensitivity to initial conditions, which makes accurate prediction challenging. Recent approaches have focused on developing data-driven…
This paper presents a new chaotic system having four attractors, including two fixed point attractors and two symmetrical chaotic strange attractors. Dynamical properties of the system, viz. sensitive dependence on initial conditions,…
Valveless pumping assists in fluid transport in various organisms and engineering systems. In a previous work, to study the actuator impact effects on valveless pumping, we constructed a piecewise-linear lumped-parameter model for a…
An attractor of a piecewise-smooth continuous system of differential equations can bifurcate from a stable equilibrium to a more complicated invariant set when it collides with a switching manifold under parameter variation. Here numerical…
In a standard bifurcation of a dynamical system, the stationary points (or more generally attractors) change qualitatively when varying a control parameter. Here we describe a novel unusual effect, when the change of a parameter, e.g. a…
Chaotic scattering in three dimensions has not received as much attention as in two dimensions so far. In this paper, we deal with a three-dimensional open Hamiltonian system whose Wada basin boundaries become non Wada when the critical…
Driven dissipative systems at ambient conditions typically exhibit continuous responses shaped by fluctuations and relaxation, with discrete macroscopic states arising only under specific dynamical constraints. Here, we report the emergence…
We prove that deterministic motion in dissipative systems emerges as a strict geometric attractor of contact flow, not a statistical approximation. Building on the contact geometry of stochastic vector bundles, we develop time-dependent…
We investigate the dynamics of chaotic trajectories in simple yet physically important Hamiltonian systems with non-hierarchical borders between regular and chaotic regions with positive measures. We show that the stickiness to the border…
Entropic Dynamics is a framework in which dynamical laws are derived as an application of entropic methods of inference. No underlying action principle is postulated. Instead, the dynamics is driven by entropy subject to the constraints…
Applying the theory of self-adjoint extensions of Hermitian operators to Koopman von Neumann classical mechanics, the most general set of probability distributions is found for which entropy is conserved by Hamiltonian evolution. A new…
In theoretical ecology, models describing the spatial dispersal and the temporal evolution of species having non-overlapping generations are often based on integrodifference equations. For various such applications the environment has an…
We consider dynamical systems given by interval maps with a finite number of turning points (including critical points, discontinuities) possibly of different critical orders from two sides. If such a map $f$ is continuous and piecewise…