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Preliminaries

Published online by Cambridge University Press:  05 March 2015

Mark Pollicott
Affiliation:
University of Manchester
Michiko Yuri
Affiliation:
Sapporo University, Japan
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Summary

1. Conventions. The book is divided into 16 chapters, each subdivided into sections numbered in order (e.g. chapter 12, section 3 is numbered 12.3).

Within each chapter results (Theorems, Propositions or Lemmas) are labelled by the chapter and then the order of occurrence (e.g. the fifth result in chapter 3 is Proposition 3.5). The exceptions to this rule are: sublemmas which are presented within the context of the proof of a more important result (e.g. the proof of Theorem 2.2 contains Sublemmas 2.2.1 and 2.2.2); and corollaries (the corollary to Theorem 5.5 is Corollary 5.5.1).

We denote the end of a proof by ▪.

Finally, equations are numbered by the chapter and their order of occurrence (e.g. the fourth equation in chapter 5 is labelled (5.4))

2. Notation. We shall use the standard notation: ℝ to denote the real numbers; ℚ to denote the rational numbers; ℤ to denote the integer numbers; ℕ to denote the natural numbers; and ℤ+ to denote the nonnegative integers. We use the convenient convention that: ℝ/ℤ = {x + ℤ : x ∈ ℝ} (which is homeomorphic to the standard unit circle); ℝ2/ℤ2 = {(x1, x2) + ℤ2 : (x1, x2) ∈ ℝ2} (which is homeomorphic to the standard 2-torus); etc. However, for x ∈ ℝ we denote the corresponding element in ℝ/ℤ by x (mod 1) (and similarly for ℝ2/ℤ2, etc.).

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Publisher: Cambridge University Press
Print publication year: 1998

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  • Preliminaries
  • Mark Pollicott, University of Manchester, Michiko Yuri, Sapporo University, Japan
  • Book: Dynamical Systems and Ergodic Theory
  • Online publication: 05 March 2015
  • Chapter DOI: https://doi.org/10.1017/CBO9781139173049.002
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  • Preliminaries
  • Mark Pollicott, University of Manchester, Michiko Yuri, Sapporo University, Japan
  • Book: Dynamical Systems and Ergodic Theory
  • Online publication: 05 March 2015
  • Chapter DOI: https://doi.org/10.1017/CBO9781139173049.002
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Preliminaries
  • Mark Pollicott, University of Manchester, Michiko Yuri, Sapporo University, Japan
  • Book: Dynamical Systems and Ergodic Theory
  • Online publication: 05 March 2015
  • Chapter DOI: https://doi.org/10.1017/CBO9781139173049.002
Available formats
×