Dynamics of certain smooth one-dimensional mappings II: geometrically finite one-dimensional mappings

Details Dynamics of certain smooth one-dimensional mappings II: geometrically finite one-dimensional mappings Dynamics of certain smooth one-dimensional mappings II: geometrically finite one-dimensional mappings

1991-01-11

arxiv.org/abs/math/9201278v1

Mathematics

Dynamical Systems

Scientific paper

We study geometrically finite one-dimensional mappings. These are a subspace of $C^{1+\alpha}$ one-dimensional mappings with finitely many, critically finite critical points. We study some geometric properties of a mapping in this subspace. We prove that this subspace is closed under quasisymmetrical conjugacy. We also prove that if two mappings in this subspace are topologically conjugate, they are then quasisymmetrically conjugate. We show some examples of geometrically finite one-dimensional mappings.

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