Devaney's chaos or 2-scattering implies Li–Yorke's chaos

@article{Huang2002DevaneysCO,
  title={Devaney's chaos or 2-scattering implies Li–Yorke's chaos},
  author={Wen Huang and Xiangdong Ye},
  journal={Topology and its Applications},
  year={2002},
  volume={117},
  pages={259-272}
}
  • Wen Huang, X. Ye
  • Published 14 February 2002
  • Mathematics
  • Topology and its Applications

Devaney's chaos implies existence of s-scrambled sets

Let X be a complete metric space without isolated points, and let f : X → X be a continuous map. In this paper we prove that if f is transitive and has a periodic point of period p, then f has a

Devaney’s and Li-Yorke’s Chaos in Uniform Spaces

A definition of chaos in the sense of Li-Yorke is given for an action of a group on a uniform space, and it is shown that if a continuous action of an Abelian group G on a second countable Baire

DISTRIBUTIONAL CHAOS REVISITED

In their famous paper, Schweizer and Smital introduced the definition of a distributionally chaotic pair and proved that the existence of such a pair implies positive topological entropy for

On Li-Yorke pairs

The Li–Yorke definition of chaos proved its value for interval maps. In this paper it is considered in the setting of general topological dynamics. We adopt two opposite points of view. On the one

Devaney's chaos revisited

The Research of G- expansive Map and Devaney’s G-Chaos Condition on Metric G-Space

The expansive map and chaos have an important significance in terms of theory and application. According to the definition of expansive map and chaos, we give the concept of G-expansive map and

ON CHAOS OF THE LOGISTIC MAPS

This paper is concerned with chaos of a family of logistic maps. It is first proved that a regular and nondegenerate snap-back repeller implies chaos in the sense of both Devaney and Li-Yorke for a
...

References

SHOWING 1-10 OF 14 REFERENCES

On Devaney's definition of chaos

Chaotic dynamical systems have received a great deal of attention in recent years (see for instance [2], [3]). Although there has been no universally accepted mathematical definition of chaos, the

On li-yorke pairs

The Li–Yorke definition of chaos proved its value for interval maps. In this paper it is considered in the setting of general topological dynamics. We adopt two opposite points of view. On the one

Asymptotic pairs in positive-entropy systems

We show that in a topological dynamical system (X,T) of positive entropy there exist proper (positively) asymptotic pairs, that is, pairs (x,y) such that x\not= y and \lim_{n\to +\infty} d(T^n x,T^n

Homeomorphisms with the whole compacta being scrambled sets

A homeomorphism on a metric space (X,d) is completely scrambled if for each x\not= y\in X, \lim sup_{n\longrightarrow +\infty} d(f^n(x),f^n(y))>0 and \lim inf_{n\ longrightarrow

A simple characterization of the set ofμ-entropy pairs and applications

AbstractWe present simple characterizations of the setsEμ andEX of measure entropy pairs and topological entropy pairs of a topological dynamical system (X, T) with invariant probability measureμ.

Residual properties and almost equicontinuity

A propertyP of a compact dynamical system (X,f) is called a residual property if it is inherited by factors, almost one-to-one lifts and surjective inverse limits. Many transitivity properties are

Sensitive dependence on initial conditions

It is shown that the property of sensitive dependence on initial conditions in the sense of Guckenheimer follows from the other two more technical parts of one of the most common recent definitions

Period Three Implies Chaos

The way phenomena or processes evolve or change in time is often described by differential equations or difference equations. One of the simplest mathematical situations occurs when the phenomenon

Minimal flows and their extensions

When is a Transitive Map Chaotic