Question

Artur Avila and Svetlana Jitomirskaya (“zhih-TOH-mer-sky-uh”) proved that if the frequency of the almost Mathieu (“maht-YEW”) operator has this property, Hofstadter’s butterfly is a Cantor set, resolving the “ten martini problem.” For the tent map with parameter 2 and Arnold’s cat map, inputs with this property give rise to [emphasize] non-periodic behavior. This property names a set of rotations that are (10[1])ergodic. A “measure” named for this property (-5[1])is at least 2 for numbers with this (-5[1])property, per Dirichlet’s (“dee-ree-KLAY’s”) approximation theorem. (-5[1])Zeta of 3 (-5[1])has this property, (-5[1])as shown (10[1])by Roger (10[1]-5[1])Apéry (10[1]-5[1])(“ah-pay-REE”). Real (-5[1])roots of integer-coefficient monic polynomials are either integers or numbers (10[2])with this property, (10[1]-5[2])the set of which is denoted by the expression “R backslash Q.” (10[4])For 10 points, (10[2])name (10[1])this property of numbers that [emphasize] cannot (10[1])be expressed as one integer over another. (10[2])■END■ (10[7])

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