In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent literature on the following subjects: transversality and generic properties like the various forms of the so-called Kupka-Smale theorem, the Closing Lemma and generic local bifurcations of functions (so-called catastrophe theory) and generic local bifurcations in 1-parameter families of dynamical systems, and notions of structural stability and moduli.
1. Introduction, 2. Complex linearization, 3. KAM Theory for circle and annulus maps, 4. KAM Theory for flows, 5. Further developments in KAM Theory, 6. Quasi-periodic bifurcations: dissipative setting, 7. Quasi-periodic bifurcation theory in other settings, 8. Further Hamiltonian KAM Theory, 9. Whitney smooth bundles of KAM tori, 10. Conclusion
Hardbound, 592 pages, publication date: OCT-2010
ISBN-13: 978-0-444-53141-4
Series: The Evolution of Modern Philosophy
Hardback (ISBN-13: 9780521766814)
Paperback (ISBN-13: 9780521747721)
4 b/w illus.
Page extent: 306 pages
Size: 228 x 152 mm
Examines the relations between logic and philosophy over the last 150 years. Logic underwent a major renaissance beginning in the nineteenth century. Cantor almost tamed the infinite, and Frege aimed to undercut Kant by reducing mathematics to logic. These achievements were threatened by the paradoxes, like Russell’s. This ferment generated excellent philosophy (and mathematics) by excellent philosophers (and mathematicians) up to World War II. This book provides a selective, critical history of the collaboration between logic and philosophy during this period. After World War II, mathematical logic became a recognized subdiscipline in mathematics departments, and consequently but unfortunately philosophers have lost touch with its monuments. This book aims to make four of them (consistency and independence of the continuum hypothesis, Post’s problem, and Morley’s theorem) more accessible to philosophers, making available the tools necessary for modern scholars of philosophy to renew a productive dialogue between logic and philosophy.
* A single source for otherwise scattered results * Written to maximize accessibility by philosophers to mathematical logic and its associated philosophical doctrines * Intended to revive the collaboration between philosophers and mathematical logicians
1. Cantor's paradise; 2. Die urwahrheiten; 3. Expeditions: which sets exist*; 4. The universe and everything; 5. Truth eludes proof; 6. Accommodating Cantor; 7. Or not; 8. The critique of pure reason; 9. The ways of the world; 10. The zoology of reality.
Hardback (ISBN-13: 9780521763943)
Paperback (ISBN-13: 9780521141000)
137 colour illus. 74 exercises
Page extent: 272 pages
Size: 228 x 152 mm
Aimed at both physics students and non-science majors, this unique book explains Einstein's special theory of relativity pictorially, using diagrams rather than equations. The diagrams guide the reader, step-by-step, from the basics of relativity to advanced topics including the addition of velocities, Lorentz contraction, time dilation, the twin paradox, Doppler shift, and Einstein's famous equation E=mc2. The distinctive figures throughout the book enable the reader to visualize the theory in a way that cannot be fully conveyed through equations alone. The illustrative explanations in this book maintain the logic and rigour necessary for physics students, yet are simple enough to be understood by non-scientists. The book also contains entertaining problems which challenge the reader's understanding of the materials covered.
* Uses unique diagrams, rather than equations, to explain Einstein’s special theory of relativity * The distinctive figures enable readers to visualize the theory in a way that cannot be fully conveyed through equations alone * Topics covered include the addition of velocities, Lorentz contraction, time dilation, the twin paradox, Doppler shift, and Einstein’s famous equation E=mc2
Preface; Part I. Kinematics: 1. Introduction; 2. Basics; 3. Galilean relativity; 4. Einsteinian relativity; 5. Causality; 6. Consequences; 7. Summary of Part I; Part II. Problems: 8. Qualitative problems; 9. Quantitative problems; Part III. Dynamics: 10. The world's most famous equation; 11. The problem; 12. Newtonian dynamics; 13. Relativistic dynamics; 14. Summary of Part III; Afterword; References; Index.
Series: Cambridge Monographs on Applied and Computational Mathematics (No. 18)
Hardback (ISBN-13: 9780521194693)
15 b/w illus. 190 exercises
Page extent: 240 pages
Size: 228 x 152 mm
Modern Computer Arithmetic focuses on arbitrary-precision algorithms for efficiently performing arithmetic operations such as addition, multiplication and division, and their connections to topics such as modular arithmetic, greatest common divisors, the Fast Fourier Transform (FFT), and the computation of elementary and special functions. Brent and Zimmermann present algorithms that are ready to implement in your favourite language, while keeping a high-level description and avoiding too low-level or machine-dependent details. The book is intended for anyone interested in the design and implementation of efficient high-precision algorithms for computer arithmetic, and more generally efficient multiple-precision numerical algorithms. It may also be used in a graduate course in mathematics or computer science, for which exercises are included. These vary considerably in difficulty, from easy to small research projects, and expand on topics discussed in the text. Solutions are available from the authors.
* Contains all the important algorithms relevant to integers, modular arithmetic, floating-point numbers and special functions * Each algorithm is presented in a form ready to implement in software * Solutions to exercises are available from the authors’ web site
Preface; Acknowledgements; Notation; 1. Integer arithmetic; 2. Modular arithmetic and the FFT; 3. Floating-point arithmetic; 4. Newton's method and function evaluation; Appendix. Implementations and pointers; Bibliography; Index.
Series: London Mathematical Society Lecture Note Series (No. 380)
Paperback (ISBN-13: 9780521169691)
40 b/w illus.
Page extent: 420 pages
Size: 228 x 152 mm
The biennial meetings at Sao Carlos have helped create a worldwide community of experts and young researchers working on singularity theory, with a special focus on applications to a wide variety of topics in both pure and applied mathematics. The tenth meeting, celebrating the 60th birthdays of Terence Gaffney and Maria Aparecida Soares Ruas, was a special occasion attracting the best known names in the area. This volume contains contributions by the attendees, including three articles written or co-authored by Gaffney himself, and survey articles on the existence of Milnor fibrations, global classifications and graphs, pairs of foliations on surfaces, and Gaffney's work on equisingularity.
* Written by leading experts in their field, including Terence Gaffney * Includes the latest results in an active area of research * Provides useful surveys of the subject
Preface C. T. C. Wall, M. C. Romero Fuster and M. Manoel; On a conjecture by A. Durfee E. Artal Bartolo, J. Carmona Ruber and A. Melle-Hernandez; On normal embedding of complex algebraic surfaces L. Birbrair, A. Fernandes and W. D. Neumann; Local Euler obstruction, old and new, II Jean-Paul Brasselet and Nivaldo G. Grulha, Jr; Branching of periodic orbits in reversible Hamiltonian systems C. A. Buzzi, L. A. Roberto and M. A. Teixeira; Topological invariance of the index of a binary differential equation L. S. Challapa; About the existence of Milnor fibrations J. L. Cisneros-Molina and R. N. Araujo dos Santos; Counting hypersurfaces invariant by one-dimensional complex foliations Mauricio Correa, Jr and Marcio G. Soares; A note on topological contact equivalence J. C. F. Costa; Bi-Lipschitz equivalence, integral closure and invariants Terence Gaffney; Solutions to PDEs and stratification conditions Terence Gaffney; Real integral closure and Milnor fibrations Terence Gaffney and R. N. Araujo dos Santos; Surfaces around closed principal curvature lines, an inverse problem R. Garcia, L. F. Mello and J. Sotomayor; Euler characteristics and atypical values Helmut A. Hamm; Answer to a question of Zariski A. Hefez and M. E. Hernandes; Projections of timelike surfaces in the de Sitter space Shyuichi Izumiya and Farid Tari; Spacelike submanifolds of codimension at most two in de Sitter space M. Kasedou; The geometry of Hopf and saddle-node bifurcations for waves of Hodgkin-Huxley type Isabel S. Labouriau and Paulo R. F. Pinto; Global classifications and graphs J. Martinez-Alfaro, C. Mendes de Jesus and M. C. Romero-Fuster; Real analytic Milnor fibrations and a strong Lojasiewicz inequality David B. Massey; An estimate of the degree of L-determinacy by the degree of A-determinacy for curve germs T. Nishimura; Regularity of the transverse intersection of two regular stratifications Patrice Orro and David Trotman; Pairs of foliations on surfaces Farid Tari; Bi-Lipschitz equisingularity David Trotman; Gaffney's work on equisingularity C. T. C. Wall; Singularities in algebraic data acquisition Y. Yomdin.