Palindromic Prefixes and Diophantine Approximation
نویسندگان
چکیده
منابع مشابه
Palindromic Prefixes and Diophantine Approximation
This text is devoted to simultaneous approximation to ξ and ξ by rational numbers with the same denominator, where ξ is an irrational non-quadratic real number. We focus on an exponent β0(ξ) that measures the regularity of the sequence of all exceptionally precise such approximants. We prove that β0(ξ) takes the same set of values as a combinatorial quantity that measures the abundance of palin...
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This text is devoted to simultaneous approximation to ξ and ξ by rational numbers with the same denominator, where ξ is a non-quadratic real number. We focus on an exponent β0(ξ) that measures the quality of such approximations (when they are exceptionally good). We prove that β0(ξ) takes the same set of values as a combinatorial quantity that measures the abundance of palindrome prefixes in an...
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Let w be an infinite word on an alphabet A. We denote by (ni)i≥1 the increasing sequence (assumed to be infinite) of all lengths of palindromic prefixes of w. In this text, we give an explicit construction of all words w such that ni+1 ≤ 2ni + 1 for all i, and study these words. Special examples include characteristic Sturmian words, and more generally standard episturmian words. As an applicat...
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The first course is devoted to the basic setup of Diophantine approximation: we start with rational approximation to a single real number. Firstly, positive results tell us that a real number x has “good” rational approximation p/q, where “good” is when one compares |x − p/q| and q. We discuss Dirichlet’s result in 1842 (see [6] Course N◦2 §2.1) and the Markoff–Lagrange spectrum ([6] Course N◦1...
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ژورنال
عنوان ژورنال: Monatshefte für Mathematik
سال: 2006
ISSN: 0026-9255,1436-5081
DOI: 10.1007/s00605-006-0425-5