Typical dynamics of plane rational maps with equal degrees

Let $f:\mathbb{CP}^2\dashrightarrow\mathbb{CP^2}$ be a rational map with algebraic and topological degrees both equal to $d\geq 2$. Little is known in general about the ergodic properties of such maps. We show here, however, that for an open set of automorphisms $T:\mathbb{CP}^2\to\mathbb{CP}^2$, the perturbed map $T\circ f$ admits exactly two ergodic measures of maximal entropy $\log d$, one of saddle and one of repelling type. Neither measure is supported in an algebraic curve, and $T\circ f$ is `fully two dimensional' in the sense that it does not preserve any singular holomorphic foliation. Absence of an invariant foliation extends to all $T$ outside a countable union of algebraic subsets. Finally, we illustrate all of our results in a more concrete particular instance connected with a two dimensional version of the well-known quadratic Chebyshev map.Comment: Many small changes in accord with referee comments and suggestion

Non-Institutional Market Making Behavior: The Dalian Futures Exchange

This paper contains three useful contributions: (1) it collects a new data-set of electronic transaction data on soybean futures from the Dalian Futures Exchange in China that records, not only the usual elements of each transaction (such as price and size) but also identifies broker and customer identities, variables not usually obtainable; (2) it presents new econometric methods for the analysis of dynamic multivariate count data based on the autoregressive conditional intensity model of Jordà and Marcellino (2000); and (3) together, the new data and econometric methods allow us to investigate, in a manner not available before, the determinants and effects of non-institutional market making (or scalping).market making, autoregressive conditional intensity, high-frequency data