33 citations · 80 across the 12 of their papers we have counts for
16 papers
On the structure of the dimension spectrum for continued fraction expansions
Painos Chitanga, Bas Lemmens, Roger Nussbaum
We analyse the dimension spectrum of continued fractions expansions with coefficients restricted to infinite subsets of . We prove that the set of powers $P_q=\{q^n\co…
Hidden Positivity and a New Approach to Numerical Computation of Hausdorff Dimension: Higher Order Methods
Richard S. Falk, Roger D. Nussbaum
In [14], the authors developed a new approach to the computation of the Hausdorff dimension of the invariant set of an iterated function system or IFS. In this paper, we extend thi…
Eigenfunctions of Perron-Frobenius Operators and a New Approach to Numerical Computation of Hausdorff Dimension: Applications in
Richard S. Falk, Roger D. Nussbaum
We develop a new approach to the computation of the Hausdorff dimension of the invariant set of an iterated function system or IFS. In the one dimensional case that we consider her…
A New Approach to Numerical Computation of Hausdorff Dimension of Iterated Function Systems: Applications to Complex Continued Fractions
Richard S. Falk, Roger D. Nussbaum
In a previous paper, dealing with "Applications in ," the authors developed a new approach to the computation of the Hausdorff dimension of the invariant set of an it…
Detecting fixed points of nonexpansive maps by illuminating the unit ball
Bas Lemmens, Brian Lins, Roger Nussbaum
We give necessary and sufficient conditions for a nonexpansive map on a finite dimensional normed space to have a nonempty, bounded set of fixed points. Among other results we show…
C^m Eigenfunctions of Perron-Frobenius Operators and a New Approach to Numerical Computation of Hausdorff Dimension
Richard S. Falk, Roger D. Nussbaum
We develop a new approach to the computation of the Hausdorff dimension of the invariant set of an iterated function system or IFS. In the one dimensional case, our methods require…