Atlas home || Conferences | Abstracts | about Atlas

Spring Topology and Dynamics Conference
March 21-23, 2002
University of Texas
Austin, TX, USA

Organizers
Cameron Gordon, John Luecke, Alan Reid

View Abstracts
Conference Homepage

A Semilinear Model for the Complex Exponential Map
by
Monica Moreno Rocha
Boston University

A Semilinear Model for the\\ Complex Exponential Map

A Semilinear Model for the
Complex Exponential Map

Robert L. Devaney and Mónica Moreno Rocha
Boston University


Abstract

The family of complex exponential functions E\lambda(z)=\lambdaez has been a source of interesting examples in Topology. We have shown in previous works the existence of indecomposable continua as proper subsets of the Julia set, when considering particular choices of real and complex parameters ([1] and [2]).

Although the dynamics of E\lambda(z) are well understood, little is known about the topology of the invariant sets afore mentioned. Also, how their topology depends on the parameter is an open question.

In this talk, we present a model over the real plane that recreates the same dynamics involved for the complex exponential family. This model is based on a one parameter family of semilinear maps, piecewise continuous. Under certain assumptions over the parameter value, we show the continuum obtained from the semilinear map resembles the one obtained for E\lambda(z). Peliminary results have been obtained for our model to explain the dependence of the topology with respect to the parameter.







References

[]
Devaney, R.L., Knaster-like continua and complex dynamics, Ergod. Th. & Dynam. Sys. 13, (1993), 627-634.

[]
Moreno Rocha, M., Existence of indecomposable continua for the unstable exponential, preprint.

Date received: March 5, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caik-85.