Nonhyperbolic step skew-products: Ergodic approximation

We study transitive step skew-product maps modeled over a complete shift of $k$, $k\ge2$, symbols whose fiber maps are defined on the circle and have intermingled contracting and expanding regions. These dynamics are genuinely nonhyperbolic and exhibit simultaneously ergodic measures with positive, negative, and zero exponents. We introduce a set of axioms for the fiber maps and study the dynamics of the resulting skew-product. These axioms turn out to capture the key mechanisms of the dynamics of nonhyperbolic robustly transitive maps with compact central leaves. Focusing on the nonhyperbolic ergodic measures (with zero fiber exponent) of these systems, we prove that such measures are approximated in the weak$\ast$ topology and in entropy by hyperbolic ones. We also prove that they are in the intersection of the convex hulls of the measures with positive fiber exponent and with negative fiber exponent. Our methods also allow us to perturb hyperbolic measures. We can perturb a measure with negative exponent directly to a measure with positive exponent (and vice-versa), however we lose some amount of entropy in this process. The loss of entropy is determined by the difference between the Lyapunov exponents of the measures.Comment: 43 pages, 5 figure

Non-factorial nodal complete intersection threefolds

We give a bound on the minimal number of singularities of a nodal projective complete intersection threefold which contains a smooth complete intersection surface that is not a Cartier divisor

Magnetic properties of Yb2Mo2O7 and Gd2Mo2O7 from rare earth Mossbauer measurements

Using 170-Yb and 155-Gd Mossbauer measurements down to 0.03K, we have examined the semiconducting pyrochlore Yb2Mo2O7 where the Mo intra-sublattice interaction is anti-ferromagnetic and the metallic pyrochlore Gd2Mo2O7 where this interaction is ferromagnetic. Additional information was obtained from susceptibility, magnetisation and 172-Yb perturbed angular correlation measurements. The microscopic measurements evidence lattice disorder which is important in Yb2Mo2O7 and modest in Gd2Mo2O7. Magnetic irreversibilities occur at 17K in Yb2Mo2O7 and at 75K in Gd2Mo2O7 and below these temperatures the rare earths carry magnetic moments which are induced through couplings with the Mo sublattice. In Gd2Mo2O7, we observe the steady state Gd hyperfine populations at 0.027K are out of thermal equilibrium, indicating that Gd and Mo spin fluctuations persist at very low temperatures. Frustration is thus operative in this essentially isotropic pyrochlore where the dominant Mo intra-sublattice interaction is ferromagnetic.Comment: 9 pages, 9 figure

Relationship Between Periodontal Screening and Recording Index Scores and Need for Periodontal Access Surgery

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/141032/1/jper1042.pd

On the Hausdorff dimension of invariant measures of weakly contracting on average measurable IFS

We consider measures which are invariant under a measurable iterated function system with positive, place-dependent probabilities in a separable metric space. We provide an upper bound of the Hausdorff dimension of such a measure if it is ergodic. We also prove that it is ergodic iff the related skew product is.Comment: 16 pages; to appear in Journal of Stat. Phy