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Knaster-like continua and complex dynamics
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AbstractIn this paper we discuss the topology and dynamics ofEλ(z) = λezwhen λ is real and λ > 1/e. It is known that the Julia set ofEλis the entire plane in this case. Our goal is to show that there are certain natural invariant subsets forEλwhich are topologically Knaster-like continua. Moreover, the dynamical behavior on these invariant sets is quite tame. We show that the only trivial kinds of α- and ω-limit sets are possible.
Title: Knaster-like continua and complex dynamics
Description:
AbstractIn this paper we discuss the topology and dynamics ofEλ(z) = λezwhen λ is real and λ > 1/e.
It is known that the Julia set ofEλis the entire plane in this case.
Our goal is to show that there are certain natural invariant subsets forEλwhich are topologically Knaster-like continua.
Moreover, the dynamical behavior on these invariant sets is quite tame.
We show that the only trivial kinds of α- and ω-limit sets are possible.
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