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

Departament d'Economia i d'Història Econòmica

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Resum

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.

Idioma original	Anglès
Pàgines (de-a)	1-12
Revista	Conformal Geometry and Dynamics
Volum	6
Número	1
DOIs	https://doi.org/10.1090/S1088-4173-02-00080-2
Estat de la publicació	Publicada - 16 de gen. 2002

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10.1090/S1088-4173-02-00080-2

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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",

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

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journal = "Conformal Geometry and Dynamics",

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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.

UR - https://www.scopus.com/pages/publications/85009802323

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

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