# Chaotic dynamics: fractals, tilings, and substitutions

##### By: Goodson, Geoffrey R

Series: Cambridge mathematical textbooksPublisher: New Delhi Cambridge University Press 2017Description: xiv, 403 pISBN: 9781107112674Subject(s): Chaotic behavior in systems | DynamicsDDC classification: 515.39 Summary: This undergraduate textbook is a rigorous mathematical introduction to dynamical systems and an accessible guide for students transitioning from calculus to advanced mathematics. It has many student-friendly features, such as graded exercises that range from straightforward to more difficult with hints, and includes concrete applications of real analysis and metric space theory to dynamical problems. Proofs are complete and carefully explained, and there is opportunity to practice manipulating algebraic expressions in an applied context of dynamical problems. After presenting a foundation in one-dimensional dynamical systems, the text introduces students to advanced subjects in the latter chapters, such as topological and symbolic dynamics. It includes two-dimensional dynamics, Sharkovsky's theorem, and the theory of substitutions, and takes special care in covering Newton's method. Mathematica code is available online, so that students can see implementation of many of the dynamical aspects of the text. Requires no prior knowledge of real analysis or metric spaces, making it an ideal transitional text between the calculus sequence and more advanced topics in real analysis and topology Offers an introduction to topological and symbolic dynamical systems that, unlike other available textbooks, is suitable for both senior undergraduates and beginning graduate students Illustrates concrete applications of real analysis and metric space theory to dynamical problems, showing students why advanced mathematics is important and useful Mathematica code is available online, so that students can see implementation of many of the dynamical aspects of the text Read more at http://www.cambridge.org/gb/academic/subjects/mathematics/differential-and-integral-equations-dynamical-systems-and-co/chaotic-dynamics-fractals-tilings-and-substitutions#r7udd6Gw46Hk71CD.99Item type | Current location | Collection | Call number | Status | Date due | Barcode |
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Books | Vikram Sarabhai Library General Stacks | Non-fiction | 515.39 G6C4 (Browse shelf) | Available | 197172 |

##### Browsing Vikram Sarabhai Library shelves, Shelving location: General Stacks, Collection: Non-fiction Close shelf browser

515.357 A8P2 Parameter estimation and inverse problems | 515.357 G6L4 Linear inverse problems and tikhonov regularization | 515.39 G5I6 An introduction to piecewise smooth dynamics | 515.39 G6C4 Chaotic dynamics: fractals, tilings, and substitutions | 515.392 P3 Perturbations, optimization, and statistics | 515.4 S9M3 Measure, integration and function spaces | 515.42 T2I6 An introduction to measure theory, Vol 126 |

This undergraduate textbook is a rigorous mathematical introduction to dynamical systems and an accessible guide for students transitioning from calculus to advanced mathematics. It has many student-friendly features, such as graded exercises that range from straightforward to more difficult with hints, and includes concrete applications of real analysis and metric space theory to dynamical problems. Proofs are complete and carefully explained, and there is opportunity to practice manipulating algebraic expressions in an applied context of dynamical problems. After presenting a foundation in one-dimensional dynamical systems, the text introduces students to advanced subjects in the latter chapters, such as topological and symbolic dynamics. It includes two-dimensional dynamics, Sharkovsky's theorem, and the theory of substitutions, and takes special care in covering Newton's method. Mathematica code is available online, so that students can see implementation of many of the dynamical aspects of the text.

Requires no prior knowledge of real analysis or metric spaces, making it an ideal transitional text between the calculus sequence and more advanced topics in real analysis and topology

Offers an introduction to topological and symbolic dynamical systems that, unlike other available textbooks, is suitable for both senior undergraduates and beginning graduate students

Illustrates concrete applications of real analysis and metric space theory to dynamical problems, showing students why advanced mathematics is important and useful

Mathematica code is available online, so that students can see implementation of many of the dynamical aspects of the text

Read more at http://www.cambridge.org/gb/academic/subjects/mathematics/differential-and-integral-equations-dynamical-systems-and-co/chaotic-dynamics-fractals-tilings-and-substitutions#r7udd6Gw46Hk71CD.99

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