Global Solvability and Simultaneously Approximable Vectors
نویسندگان
چکیده
منابع مشابه
The Geometry of Badly Approximable Vectors
A vector v = (v1, v2, . . . , vk) in R k is -badly approximable if for all m, and for 1 ≤ j ≤ k, the distance ‖mvj‖ from mvj to the nearest integer satisfies ‖mvj‖ > m−1/k. A badly approximable vector is a vector that is -badly approximable for some > 0. For the case of k = 1, these are just the badly approximable numbers, that is, the ones with a continued fraction expansion for which the part...
متن کاملBadly Approximable Numbers and Vectors in Cantor-like Sets
We show that a large class of Cantor-like sets of Rd, d ≥ 1, contains uncountably many badly approximable numbers, respectively badly approximable vectors, when d ≥ 2. An analogous result is also proved for subsets of Rd arising in the study of geodesic flows corresponding to (d+1)-dimensional manifolds of constant negative curvature and finite volume, generalizing the set of badly approximable...
متن کاملThe Set of Badly Approximable Vectors Is Strongly C Incompressible
We prove that the countable intersection of C1-diffeomorphic images of certain Diophantine sets has full Hausdorff dimension. For example, we show this for the set of badly approximable vectors in Rd, improving earlier results of Schmidt and Dani. To prove this, inspired by ideas of McMullen, we define a new variant of Schmidt’s (α, β)-game and show that our sets are hyperplane absolute winning...
متن کاملSymmetries and global solvability of the isothermal gas dynamics equations
We study the Cauchy problem associated with the system of two conservation laws arising in isothermal gas dynamics, in which the pressure and the density are related by the γ-law equation p(ρ) ∼ ρ with γ = 1. Our results complete those obtained earlier for γ > 1. We prove the global existence and compactness of entropy solutions generated by the vanishing viscosity method. The proof relies on c...
متن کاملδ-approximable Functions
In this paper we study several notions of approximability of functions in the framework of the BSS model. Denoting with φδM the function computed by a BSS machine M when its comparisons are against −δ rather than 0, we study classes of functions f for which φδM → f in some sense (pointwise, uniformly, etc.). The main equivalence results show that this notion coincides with Type 2 computability ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2002
ISSN: 0022-0396
DOI: 10.1006/jdeq.2001.4132