Related papers: Revisiting the dynamic of Q-deformed logistic maps
A new q-deformed logistic map is proposed and it is found to have concavity in parts of the x-space. Its one-cycle and two-cycle non-trivial fixed points are obtained which are found to be qualitatively and quantitatively different from…
A scheme of q-deformation of nonlinear maps is introduced. As a specific example, a q-deformation procedure related to the Tsallis q-exponential function is applied to the logistic map. Compared to the canonical logistic map, the resulting…
The delay logistic map with two types of q-deformations: Tsallis and Quantum-group type are studied. The stability of the map and its bifurcation scheme is analyzed as a function of the deformation and delay feedback parameters. Chaos is…
This study examines the Lyapunov stability under coordinate $q$-contraction and $q$-dilatation in three dynamical systems: the discrete-time dissipative H\'enon map, and the conservative, non-integrable, continuous-time H\'enon-Heiles and…
We demonstrate that the dynamics towards and within the Feigenbaum attractor combine to form a q-deformed statistical-mechanical construction. The rate at which ensemble trajectories converge to the attractor (and to the repellor) is…
We introduce a $q$-deformation that generalises in a single framework previous works on classical and enriched $P$-partitions. In particular, we build a new family of power series with a parameter $q$ that interpolates between Gessel's…
We described the $q$-deformed phase space. The $q$-deformed Hamilton eqations of motion are derived and discussed. Some simple models are considered.
Suppose that Q is a family of seminorms on a locally convex space E which determines the topology of E. We study the existence of Q-nonexpansive retractions for families of Q-nonexpansive mappings and prove that a separated and sequentially…
Starting from the basic-exponential, a q-deformed version of the exponential function established in the framework of the basic-hypergeometric series, we present a possible formulation of a generalized statistical mechanics. In a…
We solve the problem of Fourier transformation for the one-dimensional $q$-deformed Heisenberg algebra. Starting from a matrix representation of this algebra we observe that momentum and position are unbounded operators in the Hilbert…
Chaos in classical systems has been studied in plenty over many years. Although the search for chaos in quantum systems has been an area of prominent research over the last few decades, the detailed analysis of many inherently chaotic…
On the basis of the quantum q-oscillator algebra in the framework of quantum groups and non-commutative q-differential calculus, we investigate a possible q-deformation of the classical Poisson bracket in order to extend a generalized…
A method is proposed in this paper to construct a new extended q-deformed KP ($q$-KP) hiearchy and its Lax representation. This new extended $q$-KP hierarchy contains two types of q-deformed KP equation with self-consistent sources, and its…
In this paper, we consider the behaviour, when $q$ goes to $1$, of the set of a convenient basis of meromorphic solutions of a family of linear $q$-difference equations. In particular, we show that, under convenient assumptions, such basis…
We show that an infinite set of q-deformed relevant operators close a partial q-deformed Lie algebra under commutation with the Arik-Coon oscillator. The dynamics is described by the multicommutator: [H,..., [H, O]...], that follows a power…
We study the evolution of the probability density of ensembles of iterates of the logistic map that advance towards and finally remain at attractors of representative dynamical regimes. We consider the mirror families of superstable…
We introduce a new universality class of one-dimensional unimodal dissipative maps. The new family, from now on referred to as the ($z_1,z_2$)-{\it logarithmic map}, corresponds to a generalization of the $z$-logistic map. The…
Based on the spectral decomposition technique, we introduce a simple and universal numerical method to analyze the stability of solitons. Adopting this method, the linear dynamical properties of $Q$-balls are systematically revealed, from…
The $q$-deformed statistics for fermions arising within the non-extensive thermostatistical formalism has been applied to the study of various quantum many-body systems recently. The aim of the present note is to point out some subtle…
On the basis of the non-commutative q-calculus, we investigate a q-deformation of the classical Poisson bracket in order to formulate a generalized q-deformed dynamics in the classical regime. The obtained q-deformed Poisson bracket appears…