Rodney Nillsen's Books

Randomness and Recurrence in Dynamical Systems: A Real Analysis Approach

By: Rodney Nillsen

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Randomness and Recurrence in Dynamical Systems: A Real Analysis Approach

By: Rodney Nillsen

Randomness and Recurrence in Dynamical Systems aims to bridge a gap between undergraduate teaching and the research level in mathematical analysis. It makes ideas on averaging, randomness, and recurrence, which traditionally require measure theory, accessible at the undergraduate and lower graduate level. The author develops new techniques of proof and adapts known proofs to make the material accessible to students with only a background in elementary real analysis. Over 60 figures are used to explain proofs, provide alternative viewpoints and elaborate on the main text. The book explains further developments in terms of measure theory. The results are presented in the context of dynamical systems, and the quantitative results are related to the underlying qualitative phenomena—chaos, randomness, recurrence and order. The final part of the book introduces and motivates measure theory and the notion of a measurable set, and describes the relationship of Birkhoff's Individual Ergodic Theorem to the preceding ideas. Developments in other dynamical systems are indicated, in particular Lévy's result on the frequency of occurence of a given digit in the partial fractions expansion of a number.

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Page Count

376

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0883850435

ISBN 13

9780883850435

Difference Spaces and Invariant Linear Forms

By: Rodney Nillsen

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Difference Spaces and Invariant Linear Forms

By: Rodney Nillsen

Difference spaces arise by taking sums of finite or fractional differences. Linear forms which vanish identically on such a space are invariant in a corresponding sense. The difference spaces of L2 (Rn) are Hilbert spaces whose functions are characterized by the behaviour of their Fourier transforms near, e.g., the origin. One aim is to establish connections between these spaces and differential operators, singular integral operators and wavelets. Another aim is to discuss aspects of these ideas which emphasise invariant linear forms on locally compact groups. The work primarily presents new results, but does so from a clear, accessible and unified viewpoint, which emphasises connections with related work.

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Page Count

198

Publisher

Springer

Published Date

ISBN 10

3540486526

ISBN 13

9783540486527

Randomness and Recurrence in Dynamical Systems: A Real Analysis Approach

By: Rodney Nillsen

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Randomness and Recurrence in Dynamical Systems: A Real Analysis Approach

By: Rodney Nillsen

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Solve jigsaw puzzle

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Page Count

376

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0883850435

ISBN 13

9780883850435

Randomness and Recurrence in Dynamical Systems

A Real Analysis Approach

By: Rodney Nillsen

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Randomness and Recurrence in Dynamical Systems

A Real Analysis Approach

By: Rodney Nillsen

Randomness and Recurrence in Dynamical Systems makes accessible, at the undergraduate or beginning graduate level, results and ideas on averaging, randomness and recurrence that traditionally require measure theory. Assuming only a background in elementary calculus and real analysis, new techniques of proof have been developed, and known proofs have been adapted, to make this possible. The book connects the material with recent research, thereby bridging the gap between undergraduate teaching and current mathematical research. The various topics are unified by the concept of an abstract dynamical system, so there are close connections with what may be termed 'Probabilistic Chaos Theory' or 'Randomness'. The work is appropriate for undergraduate courses in real analysis, dynamical systems, random and chaotic phenomena and probability. It will also be suitable for readers who are interested in mathematical ideas of randomness and recurrence, but who have no measure theory background--

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Page Count

376

Publisher

MAA Press

Published Date

ISBN 10

161444000X

ISBN 13

9781614440000

Book's by Rodney Nillsen

Randomness and Recurrence in Dynamical Systems: A Real Analysis Approach

Randomness and Recurrence in Dynamical Systems: A Real Analysis Approach

Difference Spaces and Invariant Linear Forms

Difference Spaces and Invariant Linear Forms

Randomness and Recurrence in Dynamical Systems: A Real Analysis Approach

Randomness and Recurrence in Dynamical Systems: A Real Analysis Approach

Randomness and Recurrence in Dynamical Systems

Randomness and Recurrence in Dynamical Systems

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