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**An introduction to difference equations.
3rd ed.**
*(English)*
Zbl 1071.39001

Undergraduate Texts in Mathematics. New York, NY: Springer (ISBN 0-387-23059-9/hbk). xxii, 539 p. (2005).

The first two editions of the book (1996; Zbl 0840.39002 resp. 1999; Zbl 0930.39001 and ME 2000a.00543) are again updated by recent results on local and global stability of one-dimensional maps, on linear and nonlinear higher-order scalar difference equations, in particular, on extensions of the PoincarĂ© and Perron theorems concerning the asymptotic behaviour of solutions, and on new biological models as the larval-pupal-adult flour beetle model. Old parts of the book are rewritten, so that the new edition contains more proofs and explanations, more graphs and applications. Some of the proofs are shifted into appendices.

Unfortunately, not all errors pointed out in the reviews of the former editions, are corrected, and there appear new ones: E.g. Exercise 8.1.10 for \(g =o(f)\), the number 20 on p. \(492_{9,12}\) must be \(18\), and the solutions of Exercises 2.6.11 (replace \(2^{n-1}\) by \(2^n-1\)) and 2.6.13 are wrong.

Unfortunately, not all errors pointed out in the reviews of the former editions, are corrected, and there appear new ones: E.g. Exercise 8.1.10 for \(g =o(f)\), the number 20 on p. \(492_{9,12}\) must be \(18\), and the solutions of Exercises 2.6.11 (replace \(2^{n-1}\) by \(2^n-1\)) and 2.6.13 are wrong.

Reviewer: Lothar Berg (Rostock)

### MSC:

39Axx | Difference equations |

39-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to difference and functional equations |

39A11 | Stability of difference equations (MSC2000) |

93-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to systems and control theory |

92-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to biology |

37Jxx | Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems |

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\textit{S. N. Elaydi}, An introduction to difference equations. 3rd ed. New York, NY: Springer (2005; Zbl 1071.39001)