44 citations · 171 across the 20 of their papers we have counts for
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Badly approximable points on self-affine sponges and the lower Assouad dimension
Tushar Das, Lior Fishman, David Simmons +1
We highlight a connection between Diophantine approximation and the lower Assouad dimension by using information about the latter to show that the Hausdorff dimension of the set of…
Conformal graph directed Markov systems on Carnot groups
Vasilis Chousionis, Jeremy T. Tyson, Mariusz Urbański
We develop a comprehensive theory of conformal graph directed Markov systems in the non-Riemannian setting of Carnot groups equipped with a sub-Riemannian metric. In particular, we…
Thin annuli property and exponential distribution of return times for Weakly Markov systems
Łukasz Pawelec, Mariusz Urbański, Anna Zdunik
We deal with the problem of asymptotic distribution of first return times to shrinking balls under iteration generated by a large general class of dynamical systems called weakly M…
Badly approximable vectors and fractals defined by conformal dynamical systems
Tushar Das, Lior Fishman, David Simmons +1
We prove that if is the limit set of an irreducible conformal iterated function system (with either finite or countably infinite alphabet), then the badly approximable vectors…