Reversibility in Dynamics and Group Theory

Erscheinungsjahr 2016
ISBN: 978-1-107-44288-7
Verlag: Cambridge University Press

Buch, Englisch, Band 416, 292 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 429 g

Reihe: 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.

Autoren/Hrsg.

O'Farrell, Anthony G.

Short, Ian

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Algebra
• Mathematik | Informatik Mathematik Geometrie
• Mathematik | Informatik Mathematik Topologie
• Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen

Inhaltsverzeichnis

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.

Über Autor(innen)

Short, Ian
Ian Short is a lecturer in mathematics at the Open University. His research interests lie in dynamics and geometry.

O'Farrell, Anthony G.
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.