Reversibility in Dynamics and Group Theory

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Anthony G. O'Farrell (National University of Ireland, Maynooth) Ian Short (The Open University, Milton Keynes)

Reversibility in Dynamics and Group Theory

Anthony G. O'Farrell (National University of Ireland, Maynooth), Ian Short (The Open University, Milton Keynes)

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English

Cambridge University Press
28 May 2015

Mathematics; Algebra; Differential calculus & equations; Integral calculus & equations; Geometry

Series: London Mathematical Society Lecture Note Series

Reversibility is a thread woven through many branches of mathematics. It arises in dynamics, in systems that admit a time-reversal symmetry, and in group theory where the reversible group elements are those that are conjugate to their inverses. However, the lack of a lingua franca for discussing reversibility means that researchers who encounter the concept may be unaware of related work in other fields. This text is the first to make reversibility the focus of attention. The authors fix standard notation and terminology, establish the basic common principles, and illustrate the impact of reversibility in such diverse areas as group theory, differential and analytic geometry, number theory, complex analysis and approximation theory. As well as showing connections between different fields, the authors' viewpoint reveals many open questions, making this book ideal for graduate students and researchers. The exposition is accessible to readers at the advanced undergraduate level and above.

By: Anthony G. O'Farrell (National University of Ireland Maynooth), Ian Short (The Open University, Milton Keynes)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 416
Dimensions: Height: 229mm, Width: 152mm, Spine: 16mm
Weight: 430g
ISBN: 9781107442887
ISBN 10: 1107442885
Series: London Mathematical Society Lecture Note Series
Pages: 294
Publication Date: 28 May 2015
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Preface; 1. Origins; 2. Basic ideas; 3. Finite groups; 4. The classical groups; 5. Compact groups; 6. Isometry groups; 7. Groups of integer matrices; 8. Real homeomorphisms; 9. Circle homeomorphisms; 10. Formal power series; 11. Real diffeomorphisms; 12. Biholomorphic germs; References; List of frequently used symbols; Index of names; Subject index.

Anthony G. O'Farrell studied at Brown University and worked at the University of California, Los Angeles, then occupied the Chair of Mathematics at NUI, Maynooth for 37 years, with visiting positions in Britain, France, Spain, Israel and the USA. He is a member of the Royal Irish Academy, and has served as President of the Irish Mathematical Society. He has published four books and over 100 papers. Ian Short is a lecturer in mathematics at the Open University. His research interests lie in dynamics and geometry.