44 citations · 171 across the 20 of their papers we have counts for
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A variational principle in the parametric geometry of numbers, with applications to metric Diophantine approximation
Tushar Das, Lior Fishman, David Simmons +1
We establish a new connection between metric Diophantine approximation and the parametric geometry of numbers by proving a variational principle facilitating the computation of the…
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…
Diophantine approximation in Banach spaces
Lior Fishman, David S. Simmons, Mariusz Urbański
In this paper, we extend the theory of simultaneous Diophantine approximation to infinite dimensions. Moreover, we discuss Dirichlet-type theorems in a very general framework and d…