Nondense orbits for Anosov diffeomorphisms of the 22-torus

Let $\lambda$ denote the probability Lebesgue measure on ${\mathbb T}^2$. For any $C^2$-Anosov diffeomorphism of the $2$-torus preserving $\lambda$ 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 $C^2$-expanding maps of the circle.Comment: Minor typos corrected. Added more expositio

On circle rotations and the shrinking target properties

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

CS 156: Introduction toArtificial Intelligence Textbook Alternatives

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

We produce an estimate for the $K$-Bessel function $K_{r + i t}(y)$ with positive, real argument $y$ and of large complex order $r+it$ where $r$ is bounded and $t = y \sin \theta$ for a fixed parameter $0\leq \theta\leq \pi/2$ or $t= y \cosh \mu$ for a fixed parameter $\mu>0$. In particular, we compute the dominant term of the asymptotic expansion of $K_{r + i t}(y)$ as $y \rightarrow \infty$. When $t$ and $y$ 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 $E_0^{(j)}(z, r+it)$ for each inequivalent cusp $\kappa_j$ when $1/2 \leq r \leq 3/2$.Comment: 20 pages. The bounds for the Eisenstein series have been extended to all of $y>0$. Error terms for all the estimates have been adde

CS 156: Introduction to Artificial Intelligence Course Redesign

Poster summarizing course redesign activities for CS 156: Introduction to Artificial Intelligence.https://scholarworks.sjsu.edu/davinci_itcr2014/1016/thumbnail.jp