This book provides a broad introduction to the subject of dynamical systems, suitable for a one- or two-semester graduate course. In the first chapter, the authors introduce over a dozen examples, and then use these examples throughout the book to motivate and clarify the development of the theory. Topics include topological dynamics, symbolic dynamics, ergodic theory, hyperbolic dynamics, one-dimensional dynamics, complex dynamics, and measure-theoretic entropy. The authors top off the presentation with some beautiful and remarkable applications of dynamical systems to such areas as number theory, data storage, and Internet search engines. This book grew out of lecture notes from the graduate dynamical systems course at the University of Maryland, College Park, and reflects not only the tastes of the authors, but also to some extent the collective opinion of the Dynamics Group at the University of Maryland, which includes experts in virtually every major area of dynamical systems.

Michael Brein's travel guides make city public transport simple. Maps include how to get to the top 50 sights in the area by public transit, ultra-large transit maps, detailed mini-area maps of attractions, and instructions on how to get to places.

This volume presents a wide cross section of current research in the theory of dynamical systems and contains articles by leading researchers, including several Fields medalists, in a variety of specialties. These are surveys, usually with new results included, as well as research papers that are included because of their potentially high impact. Major areas covered include hyperbolic dynamics, elliptic dynamics, mechanics, geometry, ergodic theory, group actions, rigidity, applications. The target audience includes dynamicists, who will find new results in their own specialty as well as surveys in others, and mathematicians from other disciplines who look for a sample of current developments in ergodic theory and dynamical systems.

"Michael Brein's Guide to London by the Underground" shows travelers how to go to London's top 50 visitor attractions by the London Underground (subway, "Tube"), and some rail. The guide shows which transit to use, which lines to take, which stops to board and exit, and, using about 30 detailed mini-area-walking maps, shows exactly how to walk from these stops right to the visitor attractions. Additional nearby points of interest are also indicated on these mini-maps. An ultra-large (very easy to read) official map of the London Underground is also provided. The London guide is concise, compact, and comprehensive and fits in your pocket (leave the bulky books back in the hotel room!). \n\n

This book provides a broad introduction to the subject of dynamical systems, suitable for a one or two-semester graduate course. In the first chapter, the authors introduce over a dozen examples, and then use these examples throughout the book to motivate and clarify the development of the theory. Topics include topological dynamics, symbolic dynamics, ergodic theory, hyperbolic dynamics, one-dimensional dynamics, complex dynamics, and measure-theoretic entropy. The authors top off the presentation with some beautiful and remarkable applications of dynamical systems to areas such as number theory, data storage, and internet search engines.

Michael Brein's Guide to Berlin by the U-Bahn shows visitors how to go to Berlin's top 50 visitor attractions by the Berlin U-Bahn (subway) as well as by Berlin's S-Bahn (suburban rail system). The guide shows which transit to use, which transit stops to board and exit, and, using detailed mini-area-walking maps, how to walk exactly from these transit stops directly to the visitor attractions. Additional nearby points of interest are also indicated on these mini-area-walking maps. An ultra-large official map of the transit system is also provided. Michael Brein's Guide to Berlin is part of the world's first and only travel guide series specifically designed to show travelers how to sightsee the top 50 visitor attractions by public transportation in a variety of the world's most visited cities.