Indecomposable Continua in Exponential Dynamics
نویسنده
چکیده
In this paper we prove the existence of uncountably many indecomposable continua in the dynamics of complex exponentials of the form Eλ(z) = λe z 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.
منابع مشابه
A Semilinear Model for Exponential Dynamics and Topology
The complex exponential family Eλ(z) = λe z exhibits both rich topology and interesting dynamics. It is known that if λ is real and λ > 1/e, then Eλ admits an invariant set in the strip 0 ≤ Imz ≤ π that is an indecomposable continuum [D]. This is a closed connected set which cannot be decomposed into two (not necessarily distinct) closed, connected sets. Such sets have a complicated topological...
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