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Title:
Elephant families
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Abstract:
Parabolic implosion gives rise to 1-Complex parameter families of holomorphic maps commuting with translation by 1 and corresponding families of quotient maps called horn maps. In this project under development we study families of maps defined by 5 properties or axioms satisfied by afore mentioned maps coming from parabolic implosion of parabolic fixed points for which the immediate basin contains a unique critical point. The axioms include the finite type maps axioms of Epstein.
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