Related papers: Shadowing, chain transitive sets with nonempty int…
We examine the effects of symmetry--preserving and breaking interactions in a drive--response system where the response has an invariant symmetry in the absence of the drive. Subsequent to the onset of generalized synchronization, we find…
This paper studies set-invariance and stabilization of hyperbolic sets over rate-limited channels for discrete-time control systems. We first investigate structural and control-theoretic properties of hyperbolic sets, in particular such…
Let $f \colon X \to X$ be a continuous map on a compact metric space $X$ and let $\alpha_f$, $\omega_f$ and $ICT_f$ denote the set of $\alpha$-limit sets, $\omega$-limit sets and nonempty closed internally chain transitive sets…
It is known that hyperbolic non\-autonomous 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…
We prove that a C2 Hamiltonian system H in M is globally hyperbolic if any of the following statements holds: H is robustly topologically stable; H is stably shadowable; H is stably expansive; and H has the stable weak specification…
We present a singular perturbation theory applicable to systems with hybrid boundary layer systems and hybrid reduced systems {with} jumps from the boundary layer manifold. First, we prove practical attractivity of an adequate attractor set…
A {\em singular hyperbolic set} is a partially hyperbolic set with singularities (all hyperbolic) and volume expanding central direction \cite{MPP1}. We study connected, singular-hyperbolic, attracting sets with dense closed orbits {\em and…
We provide an alternative view of some results in [1, 3, 11]. In particular, we prove that (1) if a continuous self-map of a compact metric space has the shadowing, then the union of the basins of terminal chain components is a dense…
We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…
We prove a $C^1$ version of a conjecture by Pugh and Shub: among partially hyperbolic volume-preserving $C^r$ diffeomorphisms, $r>1$, the stably ergodic ones are $C^1$-dense. To establish these results, we develop new perturbation tools for…
We prove that any C1-stably weakly shadowable volume-preserving diffeomorphism defined on a compact manifold displays a dominated splitting E + F. Moreover, both E and F are volume-hyperbolic. Finally, we prove the version of this result…
Some nonlinear dynamical techniques, including state-space reconstruction and correlation integral, are used to analyze the light curve of 3C 273. The result is compared with a chaotic model. The similarity between them suggests that there…
We consider transition from shadow to relective scattering mode and behavior of the amplitude and cross--sections of hadron interactions in the both modes.
This paper studies the behavior of dynamical systems in non-compact spaces, specifically focusing on the concepts of global attractors and shadowing. Let $K$ be a compact global attractor. We show that the shadowing property holds in…
We introduce and study the topological concepts of chain transitivity, mixing and chain mixing property for dynamical systems induced by uniform hyperspaces. These notions generalize the relevant concepts for metric spaces.
We derive a necessary and sufficient condition for a homeomorphism with the shadowing property to be topologically transitive: to have an invariant subset $A$, dense in the non-wandering set, where the barycenter property holds. To…
We prove that a singular-hyperbolic attractor of a 3-dimensional flow is chaotic, in two strong different senses. Firstly, the flow is expansive: if two points remain close for all times, possibly with time reparametrization, then their…
We study the dynamics of phantom model and give the conditions for potentials to admit tracking attractor, de Sitter attractor and big rip attractor. Especially, we show that phantom models with exponential and inverse power law potentials…
The paper is focused on the discussion of the phenomenon of transitional chaos in dynamic autonomous and non-autonomous systems. This phenomenon involves the disappearance of chaotic oscillations in specific time periods and the system…
We expand the dynamical systems investigation of cosmological scalar fields characterised by kinetic corrections presented in [N. Tamanini, Phys. Rev. D 89 (2014) 083521]. In particular we do not restrict the analysis to exponential…