Continued Fractions: From Analytic Number Theory to by L. J. Lange, Bruce C. Berndt, Fritz Gesztesy

By L. J. Lange, Bruce C. Berndt, Fritz Gesztesy

This quantity offers the contributions from the foreign convention held on the collage of Missouri at Columbia, marking Professor Lange's seventieth birthday and his retirement from the collage. The crucial goal of the convention was once to specialise in persevered fractions as a typical interdisciplinary subject bridging gaps among various fields---from natural arithmetic to mathematical physics and approximation concept.

Evident during this paintings is the frequent effect of endured fractions in a huge variety of parts of arithmetic and physics, together with quantity concept, elliptic services, Padé approximations, orthogonal polynomials, second difficulties, frequency research, and regularity homes of evolution equations. diversified parts of present examine are represented. The lectures on the convention and the contributions to this quantity mirror the big variety of applicability of persevered fractions in arithmetic and the technologies.

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2 Strong transitivity . . . . . . . . . . . . . . . . . . 3 Topological mixture . . . . . . . . . . . . . . . . . . 4 Perfect discrete dynamical systems . . . . . . . . . . . . . . 3 Stability, Sensitivity, and Expansiveness . . . . . . . . . . . . . . . 1 Stability and instability . . . . . . . . . . . . . . . . . . . . 2 Sensitivity to the initial conditions . . . . . . . . . . . . . . 3 Expansiveness .

4 Perfect discrete dynamical systems . . . . . . . . . . . . . . 3 Stability, Sensitivity, and Expansiveness . . . . . . . . . . . . . . . 1 Stability and instability . . . . . . . . . . . . . . . . . . . . 2 Sensitivity to the initial conditions . . . . . . . . . . . . . . 3 Expansiveness . . . . . . . . . . . . . . . . . . . . . . . . . 1 Definition . . . . . . . . . . . . . . . . . . . . . .

2 Topological entropy . . . . . . . . . . . . . . . . . . 4 Properties of the topological entropy . . . . . . . . . . . . . 37 38 38 38 39 39 40 40 40 41 41 42 42 42 43 Chaotic dynamical systems have too complex behavior to be able to encompass all of their aspects using a single “perfect” definition. Indeed there exist several notions of chaos, each of them emphasize one clearly defined aspect of a chaotic behavior. The most important definitions that remain to be introduced are presented in this section.

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