Peano-type curves, Liouville numbers, and microscopic sets
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...
متن کاملLiouville numbers
In this work, we define the concept of Liouville numbers as well as the standard construction to obtain Liouville numbers and we prove their most important properties: irrationality and transcendence. This is historically interesting since Liouville numbers constructed in the standard way where the first numbers that were proven to be transcendental. The proof is very elementary and requires on...
متن کاملPeano Curves with Smooth Footprints
We construct Peano curves γ : r0,8q Ñ R2 whose “footprints” γpr0, tsq, t ą 0, have C8 boundaries and are tangent to a common continuous line field on the punctured plane R2 r tγp0qu. Moreover, these boundaries can be taken C8-close to any prescribed smooth family of nested smooth Jordan curves contracting to a point.
متن کاملExtendible Sets in Peano Arithmetic
Let sf be a structure and let U be a subset of \sf\. We say U is extendible if whenever 3S is an elementary extension of so? .there is a V Ç \£§\ such that (sf, U) -< (SS, V). Our main results are: If Jt is a countable model of Peano arithmetic and U is a subset of |-#|, then U is extendible iff U is parametrically definable in J( . Also, the cofinally extendible subsets of \J?\ are exactly the...
متن کاملInvariant Peano Curves of Expanding Thurston Maps
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: Доклады Академии наук
سال: 2019
ISSN: 0869-5652
DOI: 10.31857/s0869-565248417-10