10 research outputs found
Invariant Peano curves of expanding Thurston maps
We consider Thurston maps, i.e., branched covering maps
that are postcritically finite. In addition, we assume that is expanding in
a suitable sense. It is shown that each sufficiently high iterate of
is semi-conjugate to , where is equal to the
degree of . More precisely, for such an we construct a Peano curve
(onto), such that
(for all ).Comment: 63 pages, 12 figure
A glimpse into Thurston's work
We present an overview of some significant results of Thurston and their
impact on mathematics. The final version of this paper will appear as Chapter 1
of the book "In the tradition of Thurston: Geometry and topology", edited by K.
Ohshika and A. Papadopoulos (Springer, 2020)