Saturated Subgroups of the Circle Group

In this chapter we will discuss a technical property of being saturated in connection with subgroups of the circle group. In Chap. 11 we have seen that the group of eigenvalues of a non-singular automorphism is saturated.

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Mahendra Nadkarni

Spectral Theory of Dynamical Systems Second Edition

Texts and Readings in Mathematics Advisory Editor C. S. Seshadri, Chennai Mathematical Institute, Chennai Managing Editor Rajendra Bhatia, Ashoka University, Sonepat Editors Manindra Agrawal, Indian Institute of Technology, Kanpur V. Balaji, Chennai Mathematical Institute, Chennai R. B. Bapat, Indian Statistical Institute, New Delhi V. S. Borkar, Indian Institute of Technology, Mumbai Apoorva Khare, Indian Institute of Sciences, Bangalore T. R. Ramadas, Chennai Mathematical Institute, Chennai V. Srinivas, Tata Institute of Fundamental Research, Mumbai Technical Editor P. Vanchinathan, Vellore Institute of Technology, Chennai

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Mahendra Nadkarni

Spectral Theory of Dynamical Systems Second Edition

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Mahendra Nadkarni Emeritus Professor Department of Mathematics University of Mumbai Mumbai, Maharashtra 400098 India

ISSN 2366-8717 ISSN 2366-8725 (electronic) Texts and Readings in Mathematics ISBN 978-981-15-6224-2 ISBN 978-981-15-6225-9 (eBook) https://doi.org/10.1007/978-981-15-6225-9 Jointly published with Hindustan Book Agency The print edition is not for sale in India. Customers from India please order the print book from: Hindustan Book Agency. ISBN of the Co-Publisher’s edition: 978-93-86279-81-1 © Hindustan Book Agency 2020 and Springer Nature Singapore Pte Ltd 2020 This work is a co-publication with Hindustan Book Agency, New Delhi, licensed for sale in all countries in electronic form, in print form only outside of India. Sold and distributed in print within India by Hindustan Book Agency, 11, Zamrudpur Community Centre, Kailash Colony Extension, New Delhi 110048, India. This work is subject to copyright. All rights are reserved by the Publishers, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publishers, the authors, and the editors are safe to assume that the advice and information in this book are be