Yakov G . Sinai , Abel Prize Laureate 2014
نویسنده
چکیده
A dynamical billiard is an idealization of the game of billiard, but where the table can have shapes other than the rectangular and even be multidimensional. We use only one billiard ball, and the billiard may even have regions where the ball is kept out. Formally, a dynamical billiard is a dynamical system where a massless and point shaped particle moves inside a bounded region. The particle is reflected by specular reflections at the boundary, without loss of speed. In between two reflections the particle moves rectilinear at constant speed. Remember that a specular reflection is characterized by the law of reflection, the angle of incidence equals the angle of reflection. An example of a dynamical billiard is the so-called Sinai’s billiard. The table of the Sinai billiard is a square with a disk removed from its center; the table is flat, having no curvature
منابع مشابه
Dr. Karl Landsteiner Nobel Prize Laureate in Medicine, 1930.
Dr. Karl Landsteiner-Nobel Prize Laureate in Special Articles: Medicine, 1930: PROFESSOR STANHOPE BAYNEThe Leakage of Helium, through Pyrex Glass at JONES .. 599 Room Temperature, II: PROPESSOR G. P. BAxTER Obituary: and DR. H. W. STARKWEATHER. Increasing the Louis Hermann Panmel: PROPESSOR A. T. ERWIN. Vitamin D Potency of Cow's Milk by the Daily Memorials; Becent Deaths .604 Feeding of Irradi...
متن کاملa Billiard ? Yakov Sinai
412 NOTICES OF THE AMS VOLUME 51, NUMBER 4 Billiards are dynamical systems. In the simplest case, a “billiard table” is a compact domain Q ⊂ Rd with a piecewise smooth boundary. For a large part of the theory the class of smoothness plays no role. The reader is invited to think about components of the boundary ∂Q as subsets of C∞-submanifolds of codimension 1. The phase space M of the billiard ...
متن کاملDo Nobel Laureates Create Prize-Winning Networks? An Analysis of Collaborative Research in Physiology or Medicine
Nobel Laureates in Physiology or Medicine who received the Prize between 1969 and 2011 are compared to a matched group of scientists to examine productivity, impact, coauthorship and international collaboration patterns embedded within research networks. After matching for research domain, h-index, and year of first of publication, we compare bibliometric statistics and network measures. We fin...
متن کاملPartial Hyperbolicity, Lyapunov Exponents and Stable Ergodicity
We present some results and open problems about stable ergodicity of partially hyperbolic diffeomorphisms with nonzero Lyapunov exponents. The main tool is local ergodicity theory for non-uniformly hyperbolic systems. Dedicated to the great dynamicists David Ruelle and Yakov Sinai on their 65th birthdays
متن کامل