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Совместный общематематический семинар СПбГУ и Пекинского Университета
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Bohr chaoticity and Khintchin conjecture Aihua Fan University of Picardie Jules Verne |
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Аннотация: The Sarnak conjecture, which concerns with the Birkhoff averages weighted by the Möbius sequence, asserts that all zero entropy systems are orthogonal to the Möbius sequence. Which systems are orthogonal to none of non-trivial weights? We define such systems as Bohr chaotic systems. The Bohr chaoticity is a complexity of the system and is a topological invariant; it implies the positivity of entropy. However, the positivity of entropy doesn’t imply the Bohr chaoticity. We prove that a system Язык доклада: английский |