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Typical dynamics of plane rational maps with equal degrees
Let be a rational map with
algebraic and topological degrees both equal to . Little is known in
general about the ergodic properties of such maps. We show here, however, that
for an open set of automorphisms , the
perturbed map admits exactly two ergodic measures of maximal entropy
, one of saddle and one of repelling type. Neither measure is supported
in an algebraic curve, and is `fully two dimensional' in the sense
that it does not preserve any singular holomorphic foliation. Absence of an
invariant foliation extends to all 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
Quantum Dynamical Phase Transition in a Spin-Orbit Coupled Bose Condensate
Spin-orbit coupled bosons can exhibit rich equilibrium phases at low
temperature and in the presence of particle-particle interactions. In the case
with a 1D synthetic spin-orbit interaction, it has been observed that the
ground state of a Bose gas can be a normal phase, stripe phase, or magnetized
phase in different experimentally controllable parameter regimes. The
magnetized states are doubly degenerate and consist of a many-particle
two-state system. In this work, we investigate the nonequilibrium quantum
dynamics by switching on an external perturbation to induce resonant couplings
between the magnetized phases, and predict the novel quantum spin dynamics
which cannot be obtained in the single-particle systems. In particular, due to
particle-particle interactions, the transition of the Bose condensate from one
magnetized phase to the other is forbidden when the strength of external
perturbation is less than a critical value, and a full transition can occur
only when the perturbation exceeds such critical strength. This phenomenon
manifests itself a quantum dynamical phase transition, with the critical point
behavior being exactly solvable. From the numerical simulations and exact
analytic studies we show that the predicted many-body effects can be well
observed with the current experiments.Comment: 9 pages, 4 figures, plus supplementary materia
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
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