scholarly journals Logarithm laws for strong unstable foliations in negative curvature and non-Archimedian Diophantine approximation

2014 ◽  
Vol 8 (2) ◽  
pp. 285-309 ◽  
Author(s):  
Jayadev Athreya ◽  
Frédéric Paulin
Keyword(s):  
Diophantine Approximation ◽  
Negative Curvature ◽  
Logarithm Laws

scholarly journals Hyperbolic Center of Mass for a System of Particles in a Two-Dimensional Space with Constant Negative Curvature: An Application to the Curved 2-Body Problem

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 531
Author(s):  
Pedro Pablo Ortega Palencia ◽  
Ruben Dario Ortiz Ortiz ◽  
Ana Magnolia Marin Ramirez
Keyword(s):  
Negative Curvature ◽  
Dimensional Space ◽  
Center Of Mass ◽  
Simple Expression ◽  
Two Dimensional ◽  
Constant Negative Curvature ◽  
Euclidean Case ◽  
System Of Particles ◽  
Material Points ◽  
The One

In this article, a simple expression for the center of mass of a system of material points in a two-dimensional surface of Gaussian constant negative curvature is given. By using the basic techniques of geometry, we obtained an expression in intrinsic coordinates, and we showed how this extends the definition for the Euclidean case. The argument is constructive and serves to define the center of mass of a system of particles on the one-dimensional hyperbolic sphere LR1.

Manifolds with wells of negative curvature

1991 ◽  
Vol 103 (1) ◽  
pp. 471-495 ◽  
Author(s):  
K. D. Elworthy ◽  
Steven Rosenberg
Keyword(s):  
Negative Curvature

scholarly journals A NOTE ON WEIGHTED BADLY APPROXIMABLE LINEAR FORMS

2016 ◽  
Vol 59 (2) ◽  
pp. 349-357 ◽  
Author(s):  
STEPHEN HARRAP ◽  
NIKOLAY MOSHCHEVITIN
Keyword(s):  
Diophantine Approximation ◽  
Affirmative Answer ◽  
Famous Conjecture ◽  
Linear Forms ◽  
Badly Approximable

AbstractWe prove a result in the area of twisted Diophantine approximation related to the theory of Schmidt games. In particular, under certain restrictions we give an affirmative answer to the analogue in this setting of a famous conjecture of Schmidt from Diophantine approximation.

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