Reversibility in Dynamics and Group Theory

An accessible yet systematic account of reversibility that demonstrates its impact throughout many diverse areas of mathematics.

Anthony G. O'Farrell (Author), Ian Short (Author)

9781107442887, Cambridge University Press

Paperback / softback, published 28 May 2015

294 pages, 38 b/w illus. 11 tables
22.9 x 15.2 x 1.6 cm, 0.43 kg

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.

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.

Subject Areas: Topology [PBP], Geometry [PBM], Integral calculus & equations [PBKL], Differential calculus & equations [PBKJ], Algebra [PBF], Mathematics [PB]