Steve Alpern - Böcker

This 2000 book provides a self-contained introduction to typical properties of homeomorphisms. Examples of properties of homeomorphisms considered include transitivity, chaos and ergodicity. A key idea here is the interrelation between typical properties of volume preserving homeomorphisms and typical properties of volume preserving bijections of the underlying measure space. The authors make the first part of this book very concrete by considering volume preserving homeomorphisms of the unit n-dimensional cube, and they go on to prove fixed point theorems (Conley-Zehnder- Franks). This is done in a number of short self-contained chapters which would be suitable for an undergraduate analysis seminar or a graduate lecture course. Much of this work describes the work of the two authors, over the last twenty years, in extending to different settings and properties, the celebrated result of Oxtoby and Ulam that for volume homeomorphisms of the unit cube, ergodicity is a typical property.

This 2000 book provides a self-contained introduction to typical properties of homeomorphisms. Examples of properties of homeomorphisms considered include transitivity, chaos and ergodicity. A key idea here is the interrelation between typical properties of volume preserving homeomorphisms and typical properties of volume preserving bijections of the underlying measure space. The authors make the first part of this book very concrete by considering volume preserving homeomorphisms of the unit n-dimensional cube, and they go on to prove fixed point theorems (Conley-Zehnder- Franks). This is done in a number of short self-contained chapters which would be suitable for an undergraduate analysis seminar or a graduate lecture course. Much of this work describes the work of the two authors, over the last twenty years, in extending to different settings and properties, the celebrated result of Oxtoby and Ulam that for volume homeomorphisms of the unit cube, ergodicity is a typical property.

Search Theory is one of the classic methodological disciplines in operations research and applied mathematics. It deals with the problem faced by a searcher who wishes to minimize the time required to find a hidden object. Traditionally, the target of the search is assigned to have no motives of its own and is either stationary (for example, oil, network problems, and so on) or its motion is determined stochastically by known rules (financial markets, scheduling, genetics, and so on). This text widens the dimensions to the classical problem with the addition of an independent player of equal status to the searcher, who cares about being found or not being found. These multiple motives of searcher and hider are analytically and mathematically considered the book's two foci: Search Games (Book I) and Rendezvous Theory (Book II). Shmuel Gal's work on Search Games (Gal, 1980) stimulated considerable research in a variety of fields including Computer Science, Engineering, Biology, and Economics. New material is covered in both Search Games (Book I) and Rendezvous Theory (Book II).The book examines a whole variety of configurations of theory and problems that arise from these two aspects of the analysis - resulting in a penetrating state-of-the-art treatment of this highly useful mathematical and analytical tool.

The Theory of Search Games and Rendezvous widens the dimensions to the classical problem with the addition of an independent player of equal status to the searcher, who cares about being found or not being found. These multiple motives of searcher and hider are analytically and mathematically considered in the book's two foci: Search Games (Book I) and Rendezvous Theory (Book II). Shmuel Gal's work on Search Games (Gal, 1980) stimulated considerable research in a variety of fields including Computer Science, Engineering, Biology, and Economics. Steve Alpern's original formulation of the rendezvous search problem in 1976 and his formalization of the continuous version (Alpern, 1995) have led to much research in rendezvous theory in the past few years. New material is covered in both Search Games (Book I) and Rendezvous Theory (Book II). The book examines a whole variety of new configurations of theory and problems that arise from these two aspects of the analysis - resulting in a penetrating state-of-the-art treatment of this highly useful mathematical, analytical tool.

Search games and rendezvous problems have received growing attention in computer science within the past few years.  Rendezvous problems emerge naturally, for instance, to optimize performance and convergence of mobile robots. This gives a new algorithmic point of view to the theory. Furthermore, modern topics such as the spreading of gossip or disease in social networks have lead to new challenging problems in search and rendezvous. Search Theory: A Game Theoretic Perspective introduces the first integrated approach to Search and Rendezvous from the perspectives of  biologists, computer scientists and mathematicians. This contributed volume covers a wide range of topics including rendezvous problems and solutions, rendezvous on graphs, search games on biology, mobility in governed social networks, search and security, and more.  Most chapters also include case studies or a  survey, in addition to a chapter on the future direction of Search and Rendezvous research. This book targets researchers and practitioners working in computer science, mathematics and biology as a reference book.  Advanced level students focused on these fields will also find this book valuable as a secondary text book or reference.