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Elements of Dynamical Systems

Part of the Texts and Readings in Mathematics Book Series (volume 79)

Editors: Nagar, Anima; Shah, Riddhi; Sridharan, Shrihari

DOI: 10.1007/978-981-16-7962-9

ISBN: 978-981-16-7962-9

Publisher: Springer Nature Singapore - Springer Journals

Dec 15, 2014

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Chapter 1Real Dynamics

Kannan, V.

Pages: 1 –48

[Real dynamics is the study of those discrete dynamical systems for which the underlying set (called the phase space) is the real line R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}...
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Chapter 2Topological Dynamics

Nagar, Anima; Raja, C. R. E.

Pages: 49 –72

[Given a map f:X⟶X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f : X...
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Chapter 3Basic Ergodic Theory

Aravinda, C. S.; Bhat, Vishesh S.

Pages: 73 –107

[These notes are based on the course of six lectures given by the first named author at the well-run workshop organised at IIT-Delhi in the month of December, 2017. The lectures were intended to be self-contained covering some basic facts in ergodic theory including a discussion of the Birkhoff...
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Chapter 4Symbolic Dynamics

Bhattacharya, Siddhartha

Pages: 109 –124

[In this chapter, we will study a class of topological dynamical systems known as symbolic dynamical systems. These systems play an important role in coding theory, combinatorial dynamics and theory of cellular automata. In Sect. 2, we introduce the basic concepts associated with such systems. In...
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Chapter 5Complex Dynamics

Sridharan, S.; Verma, K.

Pages: 125 –148

[These notes are based on a set of lectures given by the second author at the Advanced Instructional School on Ergodic Theory and Dynamical Systems held at IIT Delhi in December 2017. The goal of these lectures was to introduce the audience, that comprised mainly of PhD students, to some basic...
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Chapter 6Topics in Homogeneous Dynamics and Number Theory

Ghosh, Anish

Pages: 149 –168

[This is a survey of some topics at the interface of dynamical systems and number theory, based on lectures delivered at CIRM Luminy, the University of Houston, and IIT Delhi. Specifically, we will be interested in the ergodic theory of group actions on homogeneous spaces and its connections to...
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Chapter 7On Certain Unusual Large Subsets Arising as Winning Sets of Some Games

Dani, S. G.

Pages: 169 –180

[Consider the space R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb...

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