72 citations · 178 across the 25 of their papers we have counts for
28 papers
Polygonal -subshifts
John Franks, Bryna Kra
Let be a convex polygon with each vertex in it labeled by an element from a finite set and such that the labeling of each vertex $v\in {\mathcal…
Notes on Chain Recurrence and Lyapunonv Functions
John Franks
This short expository note provides an introduction to the concept of chain recurrence in topological dynamics and a proof of the existence complete Lyapunov functions for homeomor…
Distortion and the automorphism group of a shift
Van Cyr, John Franks, Bryna Kra +1
The set of automorphisms of a one-dimensional \shift forms a countable, but often very complicated, group. For zero entropy shifts, it has recently been shown that the aut…
The spacetime of a shift endomorphism
Van Cyr, John Franks, Bryna Kra
The automorphism group of a one dimensional shift space over a finite alphabet exhibits different types of behavior: for a large class with positive entropy, it contains a rich col…
Zero entropy subgroups of mapping class groups
John Franks, Kamlesh Parwani
Let be a compact surface with boundary. We are interested in the question of how a group action on permutes a finite invariant set . More precisely, how t…
Rotation Numbers for diffeomorphisms
John Franks
These largely expository notes describe the properties of the function which assigns a number to a -tuple of distinct fixed points of an orientation preserving homeom…