Timeline for Endomorphisms of degree d on a sphere with infinite fibers on a dense subset

10 events

when toggle format	what		by	license	comment
Feb 8, 2014 at 14:34	answer	added	Peter Franek		timeline score: 1
Oct 29, 2012 at 22:22	history	edited	Hugo Chapdelaine	CC BY-SA 3.0	added 238 characters in body; edited title
Oct 29, 2012 at 22:16	history	edited	Hugo Chapdelaine		edited tags
Oct 29, 2012 at 15:11	comment	added	Hugo Chapdelaine		@Anton, I have 2 simple questions: what is the degree of your map $f$ (and how to compute it) and how do you compute a fiber $f^{-1}(y)$?
Oct 29, 2012 at 15:02	history	edited	Hugo Chapdelaine	CC BY-SA 3.0	added 70 characters in body; edited title
Oct 29, 2012 at 14:57	comment	added	Hugo Chapdelaine		Yes you are right, I had in mind something different.
Oct 29, 2012 at 0:35	comment	added	Andreas Blass		In the actual Q1 (in contrast to the title), you only asked that some point $x$ have an infinite fiber. The example you gave at the beginning of the question already does that. The set $K$ that you collapse to a point is one of the fibers of your map.
Oct 28, 2012 at 23:27	history	edited	Hugo Chapdelaine		edited tags
Oct 28, 2012 at 19:37	comment	added	Anton Petrunin		Think about the following example $f\colon \mathbb S^1\to \mathbb S^1$ defined as $$f(x)=x+\sum_n \tfrac1n\sin (n^2\cdot x) \pmod{2\cdot\pi}.$$ Note that the preimage $f^{-1}(y)$ for any $y$ is a Cantor set.
Oct 28, 2012 at 17:50	history	asked	Hugo Chapdelaine	CC BY-SA 3.0