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A new type of deterministic chaos for a system described by iterative two-dimensional maps is reported. The series being generated by the original map has an average upward trend while the first difference, which is the series of changes…
The character of the time-asymptotic evolution of physical systems can have complex, singular behavior with variation of a system parameter, particularly when chaos is involved. A perturbation of the parameter by a small amount $\epsilon$…
We study the dynamical behaviour of weighted backward shift operators defined on sequence spaces over a directed tree. We provide a characterization of chaos on very general Fr\'echet sequence spaces in terms of the existence of a large…
Recently, a concept of deterministic and stochastic turbulence has been introduced based on experiments with a boundary layer. In these experiments, the flow was driven with controlled random perturbation; in addition, natural ambient noise…
While a wealth of results has been obtained for chaos in single-particle quantum systems, much less is known about chaos in quantum many-body systems. We contribute to recent efforts to make a semiclassical analysis of such systems…
It is shown that a coupled map model for open flow may exhibit spatial chaos and spatial quasiperiodicity with temporal periodicity. The locations of these patterns, which cover a substantial part of parameter space, are indicated in a…
Relaxation in the time correlation between operators is studied. Quantized chaotic systems are shown to have distinct relaxation fluctuations that are universal and can be usefully modelled by Random Matrix Theory. Various quantized maps…
We investigate the relation between the chaotic dynamics and the hierarchical phase-space structure of generic Hamiltonian systems. We demonstrate that even in ideal situations when the phase space is dominated by an exactly self-similar…
We show that in multidimensional gravity vector fields completely determine the structure and properties of singularity. It turns out that in the presence of a vector field the oscillatory regime exists for any number of spatial dimensions…
In this letter, we show that coherent structures are related to folds of horseshoes which are present in chaotic systems. We develop techniques that allow us to construct coherent structures by manipulating folds in three prototypical…
This paper explores the chaotic properties of an advection system expressed in difference equations form. In the beginning the Aref's blinking vortex system is examined. Then several new lines are explored related to the sink problem (one…
The chaotic properties of some subshift maps are investigated. These subshifts are the orbit closures of certain non-periodic recurrent points of a shift map. We first provide a review of basic concepts for dynamics of continuous maps in…
The truly chaotic finite machines introduced by authors in previous research papers are presented here. A state of the art in this discipline, encompassing all previous mathematical investigations, is provided, explaining how finite state…
In the present study, we investigate the dynamics of impulsive differential equations driven by a chaotic system. We rigorously prove that, likewise the drive, the response impulsive system is also chaotic. Our results are based on the…
We study a new class of chaotic systems with dynamical localization, where gain or loss mechanisms break the Hermiticity, while allowing for parity-time (PT) symmetry. For a value \gamma_PT of the gain or loss parameter the spectrum…
The correlation between level velocities and eigenfunction intensities provides a new way of exploring phase space localization in quantized non-integrable systems. It can also serve as a measure of deviations from ergodicity due to quantum…
We predict synchronization of the chaotic dynamics of two atomic ensembles coupled to a heavily damped optical cavity mode. The atoms are dissipated collectively through this mode and pumped incoherently to achieve a macroscopic population…
We prove the existence of infinitely many periodic solutions and complicated dynamics, due to the presence of a topological horseshoe, for the classical Volterra predator--prey model with a periodic harvesting. The proof relies on some…
An analysis of experimental data from the RFX (Reversed Field eXperiment) reversed field pinch machine [L. Fellin, P. Kusstatscher and G. Rostagni, Fusion Eng. Des. {\bf 25}, 315 (1995)] is carried out to investigate the possible existence…
Three types of orbits are theoretically possible in autonomous Hamiltonian systems with three degrees of freedom: fully chaotic (they only obey the energy integral), partially chaotic (they obey an additional isolating integral besides…