A nilpotent IP polynomial multiple recurrence theorem

We generalize the IP-polynomial Szemer\'edi theorem due to Bergelson and McCutcheon and the nilpotent Szemer\'edi theorem due to Leibman. Important tools in our proof include a generalization of Leibman's result that polynomial mappings into a nilpotent group form a group and a multiparameter version of the nilpotent Hales-Jewett theorem due to Bergelson and Leibman.Comment: v4: switch to TeXlive 2016 and biblate

Simultaneous dense and nondense orbits for commuting maps

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.We show that, for two commuting automorphisms of the torus and for two elements of the Cartan action on compact higher rank homogeneous spaces, many points have drastically different orbit structures for the two maps. Specifically, using measure rigidity, we show that the set of points that have dense orbit under one map and nondense orbit under the second has full Hausdorff dimension.V. B. acknowledges support received from the National Science Foundation via Grant DMS-1162073 M. E. acknowledges support by the SNF (200021-152819). J. T. acknowledges the research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement n. 291147

Simultaneous dense and nondense orbits for commuting maps

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.We show that, for two commuting automorphisms of the torus and for two elements of the Cartan action on compact higher rank homogeneous spaces, many points have drastically different orbit structures for the two maps. Specifically, using measure rigidity, we show that the set of points that have dense orbit under one map and nondense orbit under the second has full Hausdorff dimension.V. B. acknowledges support received from the National Science Foundation via Grant DMS-1162073 M. E. acknowledges support by the SNF (200021-152819). J. T. acknowledges the research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement n. 291147

Form discrete- to continuous-time ergodic theorems

We introduce methods that allow to derive continuous-time versions of various discrete-time ergodic theorems. We then illustrate these methods by giving simple proofs and refinements of some known results as well as establishing new results of interest

Rigidity and Non-recurrence along Sequences

Two properties of a dynamical system, rigidity and non-recurrence, are examined in detail. The ultimate aim is to characterize the sequences along which these properties do or do not occur for different classes of transformations. The main focus in this article is to characterize explicitly the structural properties of sequences which can be rigidity sequences or non-recurrent sequences for some weakly mixing dynamical system. For ergodic transformations generally and for weakly mixing transformations in particular there are both parallels and distinctions between the class of rigid sequences and the class of non-recurrent sequences. A variety of classes of sequences with various properties are considered showing the complicated and rich structure of rigid and non-recurrent sequences

Optimization of the self-sufficient thorium fuel cycle for CANDU power reactors

The results of optimization calculations for CANDU reactors operating in the thorium cycle are presented in this paper. Calculations were performed to validate the feasibility of operating a heavy-water thermal neutron power reactor in a self-sufficient thorium cycle. Two modes of operation were considered in the paper: the mode of preliminary accumulation of 233U in the reactor itself and the mode of operation in a self-sufficient cycle. For the mode of accumulation of 233U, it was assumed that enriched uranium or plutonium was used as additional fissile material to provide neutrons for 233U production. In the self-sufficient mode of operation, the mass and isotopic composition of heavy nuclei unloaded from the reactor should provide (after the removal of fission products) the value of the multiplication factor of the cell in the following cycle K>1. Additionally, the task was to determine the geometry and composition of the cell for an acceptable burn up of 233U. The results obtained demonstrate that the realization of a self-sufficient thorium mode for a CANDU reactor is possible without using new technologies. The main features of the reactor ensuring a self-sufficient mode of operation are a good neutron balance and moving of fuel through the active core

Nonconventional Large Deviations Theorems

We obtain large deviations theorems for nonconventional sums with underlying process being a Markov process satisfying the Doeblin condition or a dynamical system such as subshift of finite type or hyperbolic or expanding transformation