Asset Details
Do you wish to reserve the book?
Continuous deformation of the Bowen-Series map associated to a cocompact triangle group
Hey, we have placed the reservation for you!
By the way, why not check out events that you can attend while you pick your title.
Oops! Something went wrong.
Looks like we were not able to place the reservation. Kindly try again later.
Are you sure you want to remove the book from the shelf?
Continuous deformation of the Bowen-Series map associated to a cocompact triangle group
Do you wish to request the book?
Continuous deformation of the Bowen-Series map associated to a cocompact triangle group
Please be aware that the book you have requested cannot be checked out. If you would like to checkout this book, you can reserve another copy
We have requested the book for you!
Your request is successful and it will be processed during the Library working hours. Please check the status of your request in My Requests.
Oops! Something went wrong.
Looks like we were not able to place your request. Kindly try again later.
Journal Article
Continuous deformation of the Bowen-Series map associated to a cocompact triangle group
2024
Overview
In 1979, for each signature for Fuchsian groups of the first kind, Bowen and Series constructed an explicit fundamental domain for one group of the signature, and from this a function on
S
1
tightly associated with this group. In general, their fundamental domain enjoys what has since been called both the ‘extension property’ and the ‘even corners property’. We determine the exact set of signatures for cocompact triangle groups for which this property can hold for any convex fundamental domain, and verify that for this restricted set, the Bowen-Series fundamental domain does have the property. To each Bowen-Series function in this corrected setting, we naturally associate four continuous deformation families of circle functions. We show that each of these functions is aperiodic if and only if it is surjective; and, is finite Markov if and only if its natural parameter is a hyperbolic fixed point of the triangle group at hand.
Publisher
Springer Netherlands,Springer Nature B.V
