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About Ergodic theory
<p>This book is about probabilistic aspects of discrete dynamical systems and</p><p>their computer simulations. Basic measure theory is used as a theoretical tool</p><p>to describe probabilistic phenomena. All of the simulations are done using the</p><p>mathematical software Maple, which enables us to translate theoretical ideas</p><p>into computer programs word by word avoiding any other technical details.</p><p>The level of familiarity with computer programming is kept minimal. Thus</p><p>even theoretical mathematicians can appreciate the experimental nature of</p><p>one of the fascinating areas in mathematics.</p><p>A new philosophy is introduced even for those who are already familiar</p><p>with numerical simulations of dynamical systems. Most computer experiments</p><p>in this book employ many significant digits depending on the entropy of the</p><p>given transformation so that they can still produce meaningful results after</p><p>many iterations. This is why we can do experiments that have not been tried</p><p>elsewhere before. It is the main point of the book. Readers should regard the</p><p>Maple programs as important as the theoretical explanations of mathematical</p><p>facts. The book is designed in such a way that theoretical and experimental</p><p>parts complement each other.</p><p>A dynamical system is a set of points together with a transformation</p><p>rule that describes the movement of points. Sometimes the points lose the</p><p>geometrical implication and they are just elements in an abstract set that has</p><p>certain structures depending on the type of the problem under consideration.</p><p>The theory of dynamical systems studies the long term statistical behavior of</p><p>the points under the transformation rules. When the given set of points has</p><p>a probabilistic structure, the theory of dynamical systems is called ergodic</p><p>theory. The aim of the book is to study computational aspects of ergodic</p><p>theory including data compression.</p><p>Many mathematical concepts introduced in the book are illustrated by</p><p>computer simulations. That gives a different flavor to ergodic theory, and</p><p>may attract a new generation of students who like to play with computers.</p><p>Some theorems look different, at least to beginners, when the abstract facts</p><p>are explained in terms of computer simulations. Many computer experiments</p>
Detailed Information
| Author: | MAGIC |
|---|---|
| Pages: | 179 |
| Language: | other |
| File Size: | 2.8023 |
| Format: | |
| Price: | FREE |
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