Dmitry Dolgopyat Giovanni Forni Rostislav Grigorchuk Boris Hasselblatt Anatole Katok Svetlana Katok Dmitry Kleinbock Raphaël Krikorian Jens Marklof
Journal of Modern Dynamics 2008, 2(1): i-v doi: 10.3934/jmd.2008.2.1i
The editors of the Journal of Modern Dynamics are happy to dedicate this issue to Gregory Margulis, who, over the last four decades, has influenced dynamical systems as deeply as few others have, and who has blazed broad trails in the application of dynamical systems to other fields of core mathematics.

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Additional editors: Leonid Polterovich, Ralf Spatzier, Amie Wilkinson and Anton Zorich.
Limit theorems for skew translations
Jory Griffin Jens Marklof
Journal of Modern Dynamics 2014, 8(2): 177-189 doi: 10.3934/jmd.2014.8.177
Bufetov, Bufetov-Forni and Bufetov-Solomyak have recently proved limit theorems for translation flows, horocycle flows and tiling flows, respectively. We present here analogous results for skew translations of a torus.
keywords: theta series. skew translation Central limit theorem
Perfect retroreflectors and billiard dynamics
Pavel Bachurin Konstantin Khanin Jens Marklof Alexander Plakhov
Journal of Modern Dynamics 2011, 5(1): 33-48 doi: 10.3934/jmd.2011.5.33
We construct semi-infinite billiard domains which reverse the direction of most incoming particles. We prove that almost all particles will leave the open billiard domain after a finite number of reflections. Moreover, with high probability the exit velocity is exactly opposite to the entrance velocity, and the particle's exit point is arbitrarily close to its initial position. The method is based on asymptotic analysis of statistics of entrance times to a small interval for irrational circle rotations. The rescaled entrance times have a limiting distribution in the limit when the length of the interval vanishes. The proof of the main results follows from the study of related limiting distributions and their regularity properties.
keywords: billiards dynamical renormalization retroreflectors. homogeneous flow Recurrence circle rotation

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