Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8905015 | Advances in Mathematics | 2018 | 29 Pages |
Abstract
The method for establishing rigorous dimension bounds involves the holomorphic extension of mappings associated to the allowed continued fraction digits, an appropriate disc which is contracted by these mappings, and an associated transfer operator acting on the Hilbert Hardy space of analytic functions on this disc. We introduce methods for rigorously bounding the approximation numbers for the transfer operators, showing that this leads to effective estimates on the Taylor coefficients of the associated determinant, and hence to explicit bounds on the Hausdorff dimension.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
O. Jenkinson, M. Pollicott,