Peano curves and smoothness of functions
نویسندگان
چکیده
منابع مشابه
Group invariant Peano curves
Our main theorem is that, if M is a closed hyperbolic 3–manifold which fibres over the circle with hyperbolic fibre S and pseudo-Anosov monodromy, then the lift of the inclusion of S in M to universal covers extends to a continuous map of B to B , where B D H [ S 1 1 . The restriction to S 1 maps onto S 1 and gives an example of an equivariant S –filling Peano curve. After proving the main theo...
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We consider Thurston maps, i.e., branched covering maps f : S → S that are postcritically finite. It is shown that a Thurston map f is expanding (in a suitable sense) if and only if some iterate F = f is semi-conjugate to z : S → S, where d = deg F . More precisely, for such an F we construct a Peano curve γ : S → S (onto), such that F ◦ γ(z) = γ(z) (for all z ∈ S).
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1980
ISSN: 0001-8708
DOI: 10.1016/0001-8708(80)90045-6