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Pisot and Salem Numbers
the attention of The publication of Charles Pisot's thesis in 1938 brought to the mathematical community those marvelous numbers now known as the Pisot numbers (or the Pisot-Vijayaraghavan numbers). Although these numbers had been discovered earlier by A. Thue and then by G. H. Hardy, it was Pisot's result in that paper of 1938 that provided the link to harmonic analysis, as discovered by Raphael Salem and described in a series of papers in the 1940s. In one of these papers, Salem introduced the related class of numbers, now universally known as the Salem numbers. These two sets of algebraic numbers are distinguished by some striking arith metic properties that account for their appearance i...
Self-similar and Self-affine Sets and Measures
Although there is no precise definition of a “fractal”, it is usually understood to be a set whose smaller parts, when magnified, resemble the whole. Self-similar and self-affine sets are those for which this resemblance is precise and given by a contracting similitude or affine transformation. The present book is devoted to this most basic class of fractal objects. The book contains both introductory material for beginners and more advanced topics, which continue to be the focus of active research. Among the latter are self-similar sets and measures with overlaps, including the much-studied infinite Bernoulli convolutions. Self-affine systems pose additional challenges; their study is often based on ergodic theory and dynamical systems methods. In the last twenty years there have been many breakthroughs in these fields, and our aim is to give introduction to some of them, often in the simplest nontrivial cases. The book is intended for a wide audience of mathematicians interested in fractal geometry, including students. Parts of the book can be used for graduate and even advanced undergraduate courses.
Acta arithmetica
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Mathematical Reviews
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Lake Pavin
This book represents the first multidisciplinary scientific work on a deep volcanic maar lake in comparison with other similar temperate lakes. The syntheses of the main characteristics of Lake Pavin are, for the first time, set in a firmer footing comparative approach, encompassing regional, national, European and international aquatic science contexts. It is a unique lake because of its permanently anoxic monimolimnion, and furthermore, because of its small surface area, its substantially low human influence, and by the fact that it does not have a river inflow. The book reflects the scientific research done on the general limnology, history, origin, volcanology and geological environment as well as on the geochemistry and biogeochemical cycles. Other chapters focus on the biology and microbial ecology whereas the sedimentology and paleolimnology are also given attention. This volume will be of special interest to researchers and advanced students, primarily in the fields of limnology, biogeochemistry, and aquatic ecology.
