13 citations · 22 across the 15 of their papers we have counts for
18 papers
Straight-line trajectories on the Mucube
Andre Oliveira, Felipe A. Ramírez, Chandrika Sadanand +1
The dynamics of straight line flows on compact half-translation surfaces (surfaces formed by gluing Euclidean polygons edge-to-edge via translations possibly composed with rotation…
Duffin--Schaeffer examples, real residue systems, and Bohr-set primes
Stefan M. Hesseling, Felipe A. Ramirez
We prove the following generalization of a well-known result of Duffin and Schaeffer: For any given countable sets and $Z\subset\mathbb{R}\setminus\operatorna…
The Duffin-Schaeffer conjecture with a moving target
Manuel Hauke, Felipe A. Ramirez
We prove the inhomogeneous generalization of the Duffin-Schaeffer conjecture in dimension . That is, given and $ψ:\mathbb{N}\to\mathbb{R}_{\g…
Metric bootstraps for limsup sets
Felipe A. Ramirez
In metric Diophantine approximation, one frequently encounters the problem of showing that a limsup set has positive or full measure. Often it is a set of points in -dimensional…
Inhomogeneous approximation for systems of linear forms with primitivity constraints
Demi Allen, Felipe A. Ramirez
We study (inhomogeneous) approximation for systems of linear forms using integer points which satisfy additional primitivity constraints. The first family of primitivity constraint…
The Duffin--Schaeffer conjecture for systems of linear forms
Felipe A. Ramirez
We extend the Duffin--Schaeffer conjecture to the setting of systems of linear forms in variables. That is, we establish a criterion to determine whether, for a given rate…
Independence inheritance and Diophantine approximation for systems of linear forms
Demi Allen, Felipe A. Ramirez
The classical Khintchine-Groshev theorem is a generalization of Khintchine's theorem on simultaneous Diophantine approximation, from approximation of points in to app…
Diophantine approximation in metric space
Jonathan M. Fraser, Henna Koivusalo, Felipe A. Ramirez
Diophantine approximation is traditionally the study of how well real numbers are approximated by rationals. We propose a model for studying Diophantine approximation in an arbitra…
Remarks about inhomogeneous pair correlations
Felipe A. Ramirez
Given an infinite subset , let denote its smallest elements. There is a rich and growing literature on the question of whether for typical $α…
Dirichlet is not just Bad and Singular
Victor Beresnevich, Lifan Guan, Antoine Marnat +2
It is well known that in dimension one the set of Dirichlet improvable real numbers consists precisely of badly approximable and singular numbers. We show that in higher dimensions…
A note on sequences not having metric Poissonian pair correlations
Felipe A. Ramirez
The purpose of this note is to present a construction of sequences which do not have metric Poissonian pair correlations (MPPC) and whose additive energies grow at rates that come…
Counterexamples, covering systems, and zero-one laws for inhomogeneous approximation
Felipe A. Ramirez
We develop the inhomogeneous counterpart to some key aspects of the story of the Duffin--Schaeffer Conjecture (1941). Specifically, we construct counterexamples to a number of cand…
Recurrence to shrinking targets on typical self-affine fractals
Henna Koivusalo, Felipe A. Ramírez
We explore the problem of finding the Hausdorff dimension of the set of points that recur to shrinking targets on a self-affine fractal. To be exact, we study the dimension of a ce…
Higher cohomology of parabolic actions on certain homogeneous spaces
Felipe A. Ramirez
We show that for a parabolic R^d-action on a compact quotient of PSL(2,R)^d, the cohomologies in degrees 1 through d-1 trivialize, and we give the obstructions to solving the degre…
Invariant distributions and cohomology for geodesic flows and higher cohomology of higher-rank Anosov actions
Felipe A. Ramirez
We are motivated by a conjecture of A. and S. Katok to study the smooth cohomologies of a family of Weyl chamber flows. The conjecture is a natural generalization of the Livshitz T…
Limit theorems for rank-one Lie groups
Alexander Gorodnik, Felipe A. Ramirez
We investigate asymptotic behaviour of averaging operators for actions of simple rank-one Lie groups. It was previously known that these averaging operators converge almost everywh…
Higher cohomology for Anosov actions on certain homogeneous spaces
Felipe A. Ramirez
We study the smooth untwisted cohomology with real coefficients for the action on [SL(2, R) \times \cdot \cdot \cdot \times SL(2, R)]/Γ by the subgroup of diagonal matrices, where…
Cocycles over higher-rank abelian actions on quotients of semisimple Lie groups
Felipe A. Ramirez
We study actions by higher-rank abelian groups on quotients of semisimple Lie groups with finite center. First, we consider actions arising from the flows of two commuting elements…