Narrow Results

We propose a model of suppression of π⁰'s based on two different effects: at low p_T we take into account the shadowing corrections, which are non-linear and essential for the description of the inclusive spectra, while at large p_T the suppression is produced through the interaction of the large p_T pion with the dense medium created in the collision. The main features of the data on AuAu and dAu collisions at RHIC energies are reproduced both at mid and at forward rapidities.

The coherence of multiscattering quark nuclear processes leads to shadowing and antishadowing of the electromagnetic nuclear structure functions in agreement with measurements. This picture leads to substantially different antishadowing for charged and neutral current processes, particularly in anti-neutrino reactions, thus affecting the extraction of the weak-mixing angle sin² θ_W.

We provide an overview of the background and recent developments in the study of the morphology evolution of thin film growth. In particular, complex non-local growth effects, including the shadowing effect and the re-emission effect, have been recently shown to significantly alter an evolving growth front. The physical principles behind these non-local effects are discussed, along with techniques used by researchers in the field to model such growth.

Shadowing of a dynamical system is often used to justify the validity of computer simulations of the system, and in numerical calculations an inverse form of the shadowing concept is also of some interest. In this paper we characterize the notion of shadowing in terms of stability, and express the notion of hyperbolicity using the concept of inverse shadowing.

We call a chaotic dynamical system pseudo-deterministic when it does not produce numerical, or pseudo-trajectories that stay close, or shadow chaotic true trajectories, even though the model equations are strictly deterministic. In this case, single chaotic trajectories may not be meaningful, and only statistical predictions, at best, could be drawn on the model, like in a stochastic system. The dynamical reason for this behavior is nonhyperbolicity characterized either by tangencies of stable and unstable manifolds or by the presence of periodic orbits embedded in a chaotic invariant set with a different number of unstable directions. We emphasize herewith the latter by studying a low-dimensional discrete-time model in which the phenomenon appears due to a saddle-repeller bifurcation. We also investigate the behavior of the finite-time Lyapunov exponents for the system, which quantifies this type of nonhyperbolicity as a system parameter evolves past a critical value. We argue that the effect of unstable dimension variability is more intense when the invariant chaotic set of the system loses transversal stability through a blowout bifurcation.

A method is proposed for the estimation of computational errors in the fixed-step integration of nonlinear systems of differential equations. This method finds the bifurcation parameters from the characteristic values of the scheme-generated discrete set and then measures the deviation from expected values at well-defined bifurcation events. With the help of some nonlinear test models, it was found that this deviation or error obeys a scaling law function of the integration step with a characteristic noninteger exponent. Our results are in agreement with previously reported errors in first order schemes. The examination of bifurcation parameters as a function of both the step and initial conditions showed the presence of several attractors where a simpler dynamics was expected. Further considerations of shadowing effects and the presence of a limiting step size are consistent with a complex build up of computational error as manifested by the scaling law.

In our paper, by using shadowing techniques, we develop a general method for establishing the existence of a transversal homoclinic orbit to a periodic orbit of diffeomorphisms in Rⁿ which implies the occurrence of chaos.

In this paper, the chaotic behavior of a set-valued mapping F : X → 2^X, where X is a compact space, is investigated. The existence of the generalized shadowing property in the hyperspace 2^X is proved. Based on the generalized shadowing property of the set-valued mappings F and the assumption of the existence of an unstable chain recurrent point of the mapping F, it is shown that the Bernoulli system of bi-directional shifts is embedded in the sense of semiconjugacy into the image of mapping F, i.e. Smale's chaos in the set-valued system F is thereby proved.

We present the following: (1) if a volume-preserving diffeomorphism has C¹-robustly various limit shadowing property, then it is Anosov; (2) C¹-generically, if a volume-preserving diffeomorphism has various limit shadowing property, then it is Anosov.

It is known that hyperbolic nonautonomous linear delay differential equations in a finite dimensional space are Hyers–Ulam stable and hence shadowable. The converse result is available only in the special case of autonomous and periodic linear delay differential equations with a simple spectrum. In this paper, we prove the converse and hence the equivalence of all three notions in the title for a general class of nonautonomous linear delay differential equations with uniformly bounded coefficients. The importance of the boundedness assumption is shown by an example.

A generalized shadowing lemma is used to study the generation of Benford sequences under non-autonomous iteration of power-like maps T_j : x ↦ α_jx^β_j (1 - f_j(x)), with α_j, β_j > 0 and f_j ∈ C¹, f_j(0) = 0, near the fixed point at x = 0. Under mild regularity conditions almost all orbits close to the fixed point asymptotically exhibit Benford's logarithmic mantissa distribution with respect to all bases, provided that the family (T_j) is contracting on average, i.e. . The technique presented here also applies if the maps are chosen at random, in which case the contraction condition reads 𝔼 log β > 0. These results complement, unify and widely extend previous work. Also, they supplement recent empirical observations in experiments with and simulations of deterministic as well as stochastic dynamical systems.

Let $X$ be a compact metric space, and let $f:X\to X$ be a homeomorphism. We show that if $f$ has the limit shadowing property then $f$ is chaotic in the sense of Li–Yorke. Moreover, $f$ is dense Li–Yorke chaos.

In this paper we study the periodic shadowing property and show that expansive dynamical systems that have the pseudo-orbit tracing property (POTP) also have the periodic shadowing. In addition, the convers is proved for chain transitive systems.

Let $f$ be a symplectic diffeomorphism on a closed $C^{\infty }$$2n$-dimensional Riemannian manifold $M$. In this paper, we show that $f$ is Anosov if any of the following statements holds: $f$ belongs to the $C^1$-interior of the set of symplectic diffeomorphisms satisfying the limit shadowing property or $f$ belongs to the $C^1$-interior of the set of symplectic diffeomorphisms satisfying the limit weak shadowing property or $f$ belongs to the $C^1$-interior of the set of symplectic diffeomorphisms satisfying the s-limit shadowing property.

In this paper, we introduce the notion of periodic shadowing property on iterated function systems, IFSs for short, and then some results will be obtained and compare with similar ones in the references. Among those results, we prove that every strongly expansive IFS with the shadowing property has the periodic shadowing property. In addition, like the shadowing property, we show that every uniformly expanding IFS has the periodic shadowing property. However, the periodic shadowing property is fulfilled for the uniformly contracting IFS provided that it is expansive.

We consider deep inelastic scattering (DIS) on a dense nucleus described as an extremal RN-AdS black hole with holographic quantum fermions in the bulk. We find that the R-ratio (the ratio of the structure function of the black hole to proton) exhibit shadowing for x < 0.1, anti-shadowing for 0.1 < x < 0.3, EMC-like effect for 0.3 < x < 0.8 and Fermi motion for x > 0.8 in a qualitative agreement with the experimental observation of the ratio for DIS on nucleus for all range of x. We also take the dilute limit of the black hole and show that its R-ratio exhibits EMC-like effect for 0.2 < x < 0.8 and the Fermi motion for x > 0.8, and no shadowing is observed in the dilute limit for both bottom-up (using Thomas-Fermi approximation for the nucleon distribution inside the dilute nucleus), and top-down (considering the dilute nucleus to be a Fermi gas in AdS) approaches.