## 266 Citations

### Devaney's chaos implies existence of s-scrambled sets

- Mathematics
- 2004

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 chaos, Li-Yorke chaos, and multi-dimensional Li-Yorke chaos for topological dynamics

- Mathematics
- 2017

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

- Mathematics
- 2017

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

- Mathematics
- 2009

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

- MathematicsJournal für die reine und angewandte Mathematik (Crelles Journal)
- 2002

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…

### The set-valued mapping induced by a non-minimal transitive system is Li–Yorke chaotic

- Mathematics
- 2009

### On strong ergodicity and chaoticity of systems with the asymptotic average shadowing property

- Mathematics
- 2011

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

- Mathematics2018 International Conference on Smart Grid and Electrical Automation (ICSGEA)
- 2018

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

- Mathematics
- 2007

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

- Mathematics
- 1992

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

- Mathematics
- 2002

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

- MathematicsErgodic Theory and Dynamical Systems
- 2002

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

- MathematicsErgodic Theory and Dynamical Systems
- 2001

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

- Mathematics
- 1997

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

- Mathematics
- 2001

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

- Mathematics
- 1993

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

- Mathematics
- 1975

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…