63,311 research outputs found

    Nondense orbits for Anosov diffeomorphisms of the 22-torus

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    Let λ\lambda denote the probability Lebesgue measure on T2{\mathbb T}^2. For any C2C^2-Anosov diffeomorphism of the 22-torus preserving λ\lambda with measure-theoretic entropy equal to topological entropy, we show that the set of points with nondense orbits is hyperplane absolute winning (HAW). This generalizes the result in~\cite[Theorem~1.4]{T4} for C2C^2-expanding maps of the circle.Comment: Minor typos corrected. Added more expositio

    What Everyone Should Know about the Copyright Law in Wonderland

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    CS 156: Introduction toArtificial Intelligence Textbook Alternatives

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    Poster summarizing cost saving textbook alternatives for CS 156: Introduction to Artificial Intelligence.https://scholarworks.sjsu.edu/davinci_tap2014/1009/thumbnail.jp

    Eisenstein series and an asymptotic for the KK-Bessel function

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    We produce an estimate for the KK-Bessel function Kr+it(y)K_{r + i t}(y) with positive, real argument yy and of large complex order r+itr+it where rr is bounded and t=ysinθt = y \sin \theta for a fixed parameter 0θπ/20\leq \theta\leq \pi/2 or t=ycoshμt= y \cosh \mu for a fixed parameter μ>0\mu>0. In particular, we compute the dominant term of the asymptotic expansion of Kr+it(y)K_{r + i t}(y) as yy \rightarrow \infty. When tt and yy are close (or equal), we also give a uniform estimate. As an application of these estimates, we give bounds on the weight-zero (real-analytic) Eisenstein series E0(j)(z,r+it)E_0^{(j)}(z, r+it) for each inequivalent cusp κj\kappa_j when 1/2r3/21/2 \leq r \leq 3/2.Comment: 20 pages. The bounds for the Eisenstein series have been extended to all of y>0y>0. Error terms for all the estimates have been adde

    On circle rotations and the shrinking target properties

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    We generalize the monotone shrinking target property (MSTP) to the s-exponent monotone shrinking target property (sMSTP) and give a necessary and sufficient condition for a circle rotation to have sMSTP. Using another variant of MSTP, we obtain a new, very short, proof of a known result, which concerns the behavior of irrational rotations and implies a logarithm law similar to D. Sullivan's logarithm law for geodesics.Comment: 13 pages. A new section has been added. The rest of the paper remains the same except for some very minor revisions
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