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Reducibility of cocycles under a Brjuno-Russmann arithmetical condition
Brjuno-Russmann arithmetical condition Dynamical Systems
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2011/9/19
Abstract: The arithmetics of the frequency and of the rotation number play a fun- damental role in the study of reducibility of analytic quasi-periodic cocycles which are sufficiently close to a const...
Arithmetical rank of squarefree monomial ideals generated by five elements or with arithmetic degree four
monomial ideal, arithmetical rank, projective dimension
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2011/8/24
Abstract: Let $I$ be a squarefree monomial ideal of a polynomial ring $S$. In this paper, we prove that the arithmetical rank of $I$ is equal to the projective dimension of $S/I$ when one of the follo...
Level statistics in arithmetical and pseudo-arithmetical chaos
arithmetical pseudo-arithmetical chaos
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2010/4/1
We resolve a long-standing riddle in quantum chaos, posed by certain fully chaotic billiards with constant negative curvature whose periodic orbits are highly degenerate in length. Depending on the bo...
On the Symmetry of Square-Free Supported Arithmetical Functions in Short Intervals
Symmetry Square-free short intervals
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2008/6/27
On the Symmetry of Square-Free Supported Arithmetical Functions in Short Intervals.