A5038766719- Mathematical Dynamics and Fractals
- Quantum chaos and dynamical systems
- Chaos control and synchronization
- Advanced Topology and Set Theory
- Advanced Differential Equations and Dynamical Systems
- Holomorphic and Operator Theory
- Advanced Banach Space Theory
- Fuzzy and Soft Set Theory
- Nonlinear Dynamics and Pattern Formation
- Advanced Algebra and Logic
- Stochastic processes and financial applications
- Geometric Analysis and Curvature Flows
- Mathematical Analysis and Transform Methods
- Fixed Point Theorems Analysis
- Mathematical and Theoretical Analysis
- Functional Equations Stability Results
- Geometry and complex manifolds
- Advanced Harmonic Analysis Research
- Stability and Controllability of Differential Equations
- Stochastic processes and statistical mechanics
- Geometric and Algebraic Topology
- Nonlinear Differential Equations Analysis
- Advanced Mathematical Theories and Applications
- Advanced Differential Geometry Research
- Diffusion and Search Dynamics
Guizhou University of Finance and Economics
2025
Southwest Petroleum University
2015-2023
University of Electronic Science and Technology of China
2011-2015
City University of Hong Kong
2013-2014
When computing a trajectory of dynamical system, influence noise can lead to large perturbations which appear, however, with small probability. Then when calculating approximate trajectories, it makes sense consider errors on average, since controlling them in each iteration may be impossible. Demand relate trajectories genuine orbits leads various notions shadowing (on average) we the paper. As main tools our studies provide few equivalent characterizations average property, also partly...
In this paper we study relations of various types sensitivity between a t.d.s. (X, T) and (M(X), TM) induced by on the space probability measures. Among other results, prove that -sensitivity implies same converse is also true when filter. We show multi-sensitive if only so -sensitive (for some/all ). finish providing an example minimal syndetically sensitive or Li–Yorke such fails to be sensitive.
For a dynamical system [Formula: see text], let text] be its induced on the space of Borel probability measures with weak*-topology. It is proved that text]-transitive (resp., exact, uniformly rigid) if and only weakly mixing rigid), where an text]-vector integers. Moreover, some analogous results are obtained for hyperspace.
An important feature of chaoticity a dynamical system [Formula: see text] is its sensitive dependence on initial conditions, which has recently been extended to concept ergodic sensitivity. This paper proves that if there exists positive integer such satisfies the large deviations theorem or ergodicity, then so text]. Moreover, iteration invariance some properties are obtained.
Let [Formula: see text] be the supremum of all topological sequence entropies a dynamical system text]. This paper obtains iteration invariance and commutativity proves that if is multisensitive transformation defined on locally connected space, then As an application, it shown Cournot map Li–Yorke chaotic only its entropy relative to suitable positive.
Some characteristics of mean sensitivity and Banach using Furstenberg families inverse limit dynamical systems are obtained. The iterated invariance proved. Applying these results, the notion is extended to uniform spaces. It proved that a point-transitive system in Hausdorff space either almost (Banach) equicontinuous or sensitive.
In this paper it is proved that the backward shift operator on Köthe sequence space admits a pair which not asymptotic, if and only has an uncountable invariant -scrambled set for some > 0, subspace scrambled linear manifold. An analogous result distributional chaos of type 2 also obtained.
At the end of his paper (Oprocha 2006 J. Phys. A: Math. Gen. 39 14 559–65), Oprocha said that it is difficult and interesting to know exact value principal measure an annihilation operator unforced quantum harmonic oscillator. Motivated by this, in this paper, we prove equal 1. Besides, point out exhibits distributional -chaos for any 0 < 2.
The aim of this paper is to study dense chaos and densely chaotic operators on Banach spaces. First, we prove that a dynamical system δ-chaotic for some δ > 0 if only it sensitive. Meanwhile, also show general systems, Devaney do not imply each other. Then, by using these results, have operator defined space, chaos, δ-chaos, generic δ-chaos are equivalent they all strictly stronger than Li-Yorke chaos.
This paper mainly discusses how Devaney chaos and Li-Yorke sensitivity carry over to product systems. First, two results on the periodic points of systems are obtained. By using them, following Proved: (1) A finite system is mixing chaotic if only each factor chaotic. (2) An infinite map Π i =1 ∞ f sup {min P( ): ∈ ℕ} < + ∞, where ) set all periods . Besides, we obtain that sensitive (sensitive) there exists a (sensitive).
We give necessary and sufficient conditions for the translation -semigroup on weighted -spaces to be chaotic in sense of Li–Yorke.
Some characterizations on the chain recurrence, transitivity, mixing property,shadowing and $h$-shadowing for Zadeh's extension are obtained. Besides, it is provedthat a dynamical system spatiotemporally chaotic provided that extensionis Li-Yorke sensitive.
In this paper, it is proved that the product system (X × Y, T S) multi-F -sensitive (resp., (F 1 , F 2 )sensitive) if and only (X, ) or (Y, )-sensitive) when Furstehberg families have Ramsey property, improving main results in [N.Deǧirmenci, S ¸.