Recurrence and higher ergodic properties for quenched random Lorentz tubes in dimension bigger than two

We consider the billiard dynamics in a non-compact set of ℝ d that is constructed as a bi-infinite chain of translated copies of the same d-dimensional polytope. A random configuration of semi-dispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global realization of the scatterers, is called quenched random Lorentz tube. Under some fairly general conditions, we prove that every system in the ensemble is hyperbolic and almost every system is recurrent, ergodic, and enjoys some higher chaotic properties.

Recurrence for quenched random Lorentz tubes

We consider the billiard dynamics in a striplike set that is tessellated by countably many translated copies of the same polygon. A random configuration of semidispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global choice of scatterers, is called quenched random Lorentz tube. We prove that under general conditions, almost every system in the ensemble is recurrent.

Spatio-temporal variability of polynya dynamics and ice production in the Laptev Sea between the winters of 1979/80 and 2007/08

Polynyas in the Laptev Sea are examined with respect to recurrence and interannual wintertime ice production.We use a polynya classification method based on passive microwave satellite data to derive daily polynya area from long-term sea-ice concentrations. This provides insight into the spatial and temporal variability of open-water and thin-ice regions on the Laptev Sea Shelf. Using thermal infrared satellite data to derive an empirical thin-ice distribution within the thickness range from 0 to 20 cm, we calculate daily average surface heat loss and the resulting wintertime ice formation within the Laptev Sea polynyas between 1979 and 2008 using reanalysis data supplied by the National Centers for Environmental Prediction, USA, as atmospheric forcing. Results indicate that previous studies significantly overestimate the contribution of polynyas to the ice production in the Laptev Sea. Average wintertime ice production in polynyas amounts to approximately 55 km39 27% and is mostly determined by the polynya area, wind speed and associated large-scale circulation patterns. No trend in ice production could be detected in the period from 1979/80 to 2007/08.