Monotone quotients of surface diffeomorphisms
Abstract
A homeomorphism of a compact metric space is tight provided every non-degenerate compact connected (not necessarily invariant) subset carries positive entropy. It is shown that every C1+α diffeomorphism of a closed surface factors to a tight homeomorphism of a generalized cactoid (roughly, a surface with nodes) by a semi-conjugacy whose fibers carry zero entropy.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.