83 citations · 293 across the 29 of their papers we have counts for
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Determinacy and indeterminacy of games played on complete metric spaces
Lior Fishman, Tue Ly, David S. Simmons
Schmidt's game is a powerful tool for studying properties of certain sets which arise in Diophantine approximation theory, number theory, and dynamics. Recently, many new results h…
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…
Diophantine approximation and the geometry of limit sets in Gromov hyperbolic metric spaces
Lior Fishman, David S. Simmons, Mariusz Urbański
In this paper, we provide a complete theory of Diophantine approximation in the limit set of a group acting on a Gromov hyperbolic metric space. This summarizes and completes a lon…