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Author: Felix Schlenk Publisher: Walter de Gruyter ISBN: 3110199696 Category : Mathematics Languages : en Pages : 261
Book Description
Symplectic geometry is the geometry underlying Hamiltonian dynamics, and symplectic mappings arise as time-1-maps of Hamiltonian flows. The spectacular rigidity phenomena for symplectic mappings discovered in the last two decades show that certain things cannot be done by a symplectic mapping. For instance, Gromov's famous "non-squeezing'' theorem states that one cannot map a ball into a thinner cylinder by a symplectic embedding. The aim of this book is to show that certain other things can be done by symplectic mappings. This is achieved by various elementary and explicit symplectic embedding constructions, such as "folding", "wrapping'', and "lifting''. These constructions are carried out in detail and are used to solve some specific symplectic embedding problems. The exposition is self-contained and addressed to students and researchers interested in geometry or dynamics.
Author: Felix Schlenk Publisher: Walter de Gruyter ISBN: 3110199696 Category : Mathematics Languages : en Pages : 261
Book Description
Symplectic geometry is the geometry underlying Hamiltonian dynamics, and symplectic mappings arise as time-1-maps of Hamiltonian flows. The spectacular rigidity phenomena for symplectic mappings discovered in the last two decades show that certain things cannot be done by a symplectic mapping. For instance, Gromov's famous "non-squeezing'' theorem states that one cannot map a ball into a thinner cylinder by a symplectic embedding. The aim of this book is to show that certain other things can be done by symplectic mappings. This is achieved by various elementary and explicit symplectic embedding constructions, such as "folding", "wrapping'', and "lifting''. These constructions are carried out in detail and are used to solve some specific symplectic embedding problems. The exposition is self-contained and addressed to students and researchers interested in geometry or dynamics.
Author: Arnold Palmer Publisher: Simon and Schuster ISBN: 145160419X Category : Sports & Recreation Languages : en Pages : 260
Book Description
It was a moment seen by millions on television. During play at the 1999 Phoenix Open, Tiger Woods had a "loose impediment? removed to play his shot -- an everyday occurrence under golf's rules. But that impediment was not a leaf or twig, it was a 350-pound boulder that took six people to move! The gallery and television audience buzzed with disbelief. How could this be legal under the rules? Indeed it could, says golf legend Arnold Palmer, who throughout his distinguished career has taken part in a sizable share of rules controversies. Despite the fact that golf has fewer rules than such sports as baseball or football or rugby, it is a contest of honor, and all players, be they tour professionals or casual weekend hackers, respect the rules. But, as Palmer points out, sometimes the rules are a little confusing -- and from time to time, even the pros are puzzled. When exactly is a ball considered "lost?? How is "slow play? defined? And when is a "drop? allowed? Palmer helps makes sense of it all with simple-to-understand language and hundreds of "infamous? pictures of some of the more controversial rulings -- affording readers a visual recall of memorable moments involving Greg Norman, Lee Janzen, Mark O'Meara, John Daly, even Palmer himself. If you're one of the millions who taketo the links every year, need a clear explanation of all the rules of the game you love, and more important, don't want to be speechless when an argument over the "coefficient of restitution? pops up, then Playing By The Rules will be an invaluable guide you'll refer to time and again.
Author: Publisher: Union Square & Co. ISBN: 1402774451 Category : Sports & Recreation Languages : en Pages : 310
Book Description
Forget the birds, the flowers, and April showers: in golf, you know spring has sprung when the Masters rolls around. Held on the hallowed grounds of the Augusta National Golf Club, and widely broadcast on TV, it’s one of the world’s most-watched sporting events each year. This collection celebrates that famed tournament, as some of America’s best known sportswriters—such as Grantland Rice and Jim Murray—praise the event’s illustrious history and traditions. The Masters has provided the stage for golf’s most prominent names, and they’re all represented on these pages, from Gene Sarazen and Ben Hogan to Arnold Palmer and Jack Nicklaus to Tiger Woods. Fans (many of whom dream of playing it themselves) will take a ride down memory and Magnolia Lane, as they recall great moments in golf, and find out about some of the quirkier, behind-the scene moments, both touching and humorous. MASTERS’ FACTS AND FIGURES: • 43 million Americans watched Tiger Woods win his first of four green jackets. • It’s the number one televised golf tournament in the world. • You cannot apply for membership; you must be invited. • The tradition of wearing green jackets began in 1937. • Dwight D. Eisenhower was the only president to have been a club member.
Author: Dusa McDuff Publisher: Oxford University Press ISBN: 0198794894 Category : Mathematics Languages : en Pages : 637
Book Description
Over the last number of years powerful new methods in analysis and topology have led to the development of the modern global theory of symplectic topology, including several striking and important results. This new third edition of a classic book in the feild includes updates and new material to bring the material right up-to-date.
Author: Jonny Evans Publisher: Cambridge University Press ISBN: 1009372661 Category : Mathematics Languages : en Pages : 242
Book Description
Symington's almost toric fibrations have played a central role in symplectic geometry over the past decade, from Vianna's discovery of exotic Lagrangian tori to recent work on Fibonacci staircases. Four-dimensional spaces are of relevance in Hamiltonian dynamics, algebraic geometry, and mathematical string theory, and these fibrations encode the geometry of a symplectic 4-manifold in a simple 2-dimensional diagram. This text is a guide to interpreting these diagrams, aimed at graduate students and researchers in geometry and topology. First the theory is developed, and then studied in many examples, including fillings of lens spaces, resolutions of cusp singularities, non-toric blow-ups, and Vianna tori. In addition to the many examples, students will appreciate the exercises with full solutions throughout the text. The appendices explore select topics in more depth, including tropical Lagrangians and Markov triples, with a final appendix listing open problems. Prerequisites include familiarity with algebraic topology and differential geometry.
Author: Marta D'Elia Publisher: SIAM ISBN: 161197805X Category : Mathematics Languages : en Pages : 187
Book Description
The book presents the state of the art of nonlocal modeling and discretization and provides a practical introduction to nonlocal modeling for readers who are not familiar with such models. These models have recently become a viable alternative to classical partial differential equations when the latter are unable to capture effects such as discontinuities and multiscale behavior in a system of interest. Because of their integral nature, nonlocal operators allow for the relaxation of regularity requirements on the solution and thus allow for the capture of multiscale effects, the result of which is their successful use in many scientific and engineering applications. The book also provides a thorough analysis and numerical treatment of nonstandard nonlocal models, focusing on both well-known and nonstandard interaction neighborhoods. In addition, the book delivers an extensive practical treatment of the implementation of discretization strategies via finite element methods. Numerous figures are provided as concrete examples to illustrate both the analytic and computational results. Nonlocal Integral Equation Continuum Models: Nonstandard Interaction Neighborhoods and Finite Element Discretizations is intended for mathematical and application researchers interested in alternatives to using partial differential equation models that better describe the phenomena they are interested in. The book will also be of use to computational scientists and engineers who need to make sense of how to use available software, improve existing software, or develop new software tailored to their application interests.
Author: Felix Schlenk
Author: Felix Schlenk
Author: United States. Army. Ordnance Department
Author: Stefan Behrens
Author: Arnold Palmer
Author: United States. Patent and Trademark Office
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Author: Dusa McDuff
Author: Jonny Evans
Author: Marta D'Elia