Indecomposable continua in exponential dynamics

Robert L. Devaney; Xavier Jarque

doi:10.1090/S1088-4173-02-00080-2

Indecomposable continua in exponential dynamics

Robert L. Devaney, Xavier Jarque

Department of Economics and Economic History

Research output: Contribution to journal › Article › Research › peer-review

21 Citations (Scopus)

Abstract

In this paper we prove the existence of uncountably many indecomposable continua in the dynamics of complex exponentials of the form Eλ(z) = λez with λ 1/e. These continua contain points that share the same itinerary under iteration of Eλ. These itineraries are bounded but consist of blocks of 0's whose lengths increase, and hence these continua are never periodic. © 2002 American Mathematical Society.

Original language	English
Pages (from-to)	1-12
Journal	Conformal Geometry and Dynamics
Volume	6
Issue number	1
DOIs	https://doi.org/10.1090/S1088-4173-02-00080-2
Publication status	Published - 16 Jan 2002

Access to Document

10.1090/S1088-4173-02-00080-2

Cite this

@article{2f8a72666e7a4c71b60a778400ad0f9d,

title = "Indecomposable continua in exponential dynamics",

abstract = "In this paper we prove the existence of uncountably many indecomposable continua in the dynamics of complex exponentials of the form Eλ(z) = λez with λ 1/e. These continua contain points that share the same itinerary under iteration of Eλ. These itineraries are bounded but consist of blocks of 0's whose lengths increase, and hence these continua are never periodic. {\textcopyright} 2002 American Mathematical Society.",

author = "Devaney, {Robert L.} and Xavier Jarque",

year = "2002",

month = jan,

day = "16",

doi = "10.1090/S1088-4173-02-00080-2",

language = "English",

volume = "6",

pages = "1--12",

journal = "Conformal Geometry and Dynamics",

issn = "1088-4173",

publisher = "American Mathematical Society",

number = "1",

}

TY - JOUR

T1 - Indecomposable continua in exponential dynamics

AU - Devaney, Robert L.

AU - Jarque, Xavier

PY - 2002/1/16

Y1 - 2002/1/16

N2 - In this paper we prove the existence of uncountably many indecomposable continua in the dynamics of complex exponentials of the form Eλ(z) = λez with λ 1/e. These continua contain points that share the same itinerary under iteration of Eλ. These itineraries are bounded but consist of blocks of 0's whose lengths increase, and hence these continua are never periodic. © 2002 American Mathematical Society.

AB - In this paper we prove the existence of uncountably many indecomposable continua in the dynamics of complex exponentials of the form Eλ(z) = λez with λ 1/e. These continua contain points that share the same itinerary under iteration of Eλ. These itineraries are bounded but consist of blocks of 0's whose lengths increase, and hence these continua are never periodic. © 2002 American Mathematical Society.

U2 - 10.1090/S1088-4173-02-00080-2

DO - 10.1090/S1088-4173-02-00080-2

M3 - Article

SN - 1088-4173

VL - 6

SP - 1

EP - 12

JO - Conformal Geometry and Dynamics

JF - Conformal Geometry and Dynamics

IS - 1

ER -

Indecomposable continua in exponential dynamics

Abstract

Access to Document

Fingerprint

Cite this