## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- Electronic Research Announcements
- Conference Publications
- AIMS Mathematics

DCDS

We study the problem of invisibility for bodies with a mirror
surface in the framework of geometrical optics. We show that
for any two given directions it is possible to construct a
two-dimensional fractal body invisible in these directions.
Moreover, there exists a three-dimensional fractal body
invisible in three orthogonal directions. The work continues
the previous study in [1,12],
where two-dimensional bodies invisible in one direction and
three-dimensional bodies invisible in one and two orthogonal
directions were constructed.

DCDS

Retroreflectors are optical devices that reverse the direction of incident beams of light. Here we present a collection of billiard type retroreflectors consisting of four objects; three of them are asymptotically perfect retroreflectors, and the fourth one is a retroreflector which is very close to perfect. Three objects of the collection have recently been discovered and published or submitted for publication. The fourth object ---

*notched angle*--- is a new one; a proof of its retroreflectivity is given.
JMD

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

## Year of publication

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