Related papers: Dynamics of composition operators induced by odome…
The concept of fundamental dynamic uncertainty (multivaluedness) developed in Parts I-III of this work and used to establish the consistent understanding of genuine chaos in Hamiltonian systems provides also causal description of the…
In quantum mechanics, measurements are dynamical processes and thus they should be capable of inducing currents. The symmetries of the Hamiltonian and measurement operator provide an organizing principle for understanding the conditions for…
In this paper we characterize mixing composition operators acting on the space $\mathscr{O}_M(\mathbb{R})$ of slowly increasing smooth functions. Moreover we relate the mixing property of those operators with the solvability of Abel's…
In this paper, we study weighted composition operators on Bergman spaces of analytic functions which are square integrable on polydisk. We develop the study in full generality, meaning that the corresponding weighted composition operators…
We propose a formalism which defines chaos in both quantum and classical systems in an equivalent manner by means of \textit{adiabatic transformations}. The complexity of adiabatic transformations which preserve classical time-averaged…
Weak values are usually associated with weak measurements of an observable on a pre- and post-selected ensemble. We show that more generally, weak values are proportional to the correlation between two pointers in a successive measurement.…
How classical chaos emerges from quantum mechanics remains a central open question, as the unitary evolution of isolated quantum systems forbids exponential sensitivity to initial conditions. A key insight is that this quantum-classical…
We show that a composition operator induced by an analytic self-map of the unit disc in the complex plane is weakly compact on the space BMOA precisely when the operator is compact on BMOA. As a crucial step we simplify the compactness…
We study the classical and quantum oscillator in the context of a non-additive (deformed) displacement operator, associated with a position-dependent effective mass, by means of the supersymmetric formalism. From the supersymmetric partner…
This work presents new tools for studying reachability and set invariance for continuous-time mixed-monotone dynamical systems subject to a disturbance input. The vector field of a mixed-monotone system is decomposable via a decomposition…
In this study, we investigate the boundedness of composition operators acting on Morrey spaces and weak Morrey spaces. The primary aim of this study is to investigate a necessary and sufficient condition on the boundedness of the…
In this paper, we deal with the construction of holomorphic functions on a simply connected domain satisfying that all its derivatives and antiderivatives under a composition operator have a dense orbit. Such functions will be called Luh…
We provide an alternative proof to those by Shkarin and by Bayart and Matheron that the operator $D$ of complex differentiation supports a hypercyclic algebra on the space of entire functions. In particular we obtain hypercyclic algebras…
In this paper, we characterize the synchronization phenomenon of hyperchaotic scalar non-linear delay dynamics in a fully-developed chaos regime. Our results rely on the observation that, in that regime, the stationary statistical…
We establish the emergence of chaotic motion in optomechanical systems. Chaos appears at negative detuning for experimentally accessible values of the pump power and other system parameters. We describe the sequence of period doubling…
The destruction of a chaotic attractor leading to rough changes in the dynamics of a dynamical system is studied. Local bifurcations are characterised by a single or a pair of characteristic exponents crossing the imaginary axis. The…
We present a decomposition of the Koopman operator based on the sparse structure of the underlying dynamical system, allowing one to consider the system as a family of subsystems interconnected by a graph. Using the intrinsic properties of…
Physical systems are often neither completely closed nor completely open, but instead they are best described by dynamical systems with partial escape or absorption. In this paper we introduce classical measures that explain the main…
Cycling chaos is a heteroclinic connection between several chaotic attractors, at which switching between the chaotic sets occur at growing time intervals. Here we characterize the coherence properties of these switchings, considering…
Complex, oscillatory data arises from a large variety of biological, physical, and social systems. However, the inherent oscillation and ubiquitous noise pose great challenges to current methodology such as linear and nonlinear time series…