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Two types of seemingly unrelated extension problems are discussed in this book. Their common focus is a long-standing problem of Johannes de Groot, the main conjecture of which was recently resolved. As is true of many important conjectures, a wide range of mathematical investigations had developed, which have been grouped into the two extension problems. The first concerns the extending of spaces, the second concerns extending the theory of dimension by replacing the empty space with other spaces. The problem of de Groot concerned compactifications of spaces by means of an adjunction of a s

Dimension theory (Topology) --- Mappings (Mathematics) --- Compactifications.

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Differential geometry. Global analysis --- Fractals --- Fractales --- Fractals. --- 517.987 --- #WBIB:dd.Lic.L.De Busschere --- Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- 517.987 Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology)

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This book develops deterministic chaos and fractals from the standpoint of iterated maps, but the emphasis makes it very different from all other books in the field. It provides the reader with an introduction to more recent developments, such as weak universality, multifractals, and shadowing, as well as to older subjects like universal critical exponents, devil's staircases and the Farey tree. The author uses a fully discrete method, a 'theoretical computer arithmetic', because finite (but not fixed) precision cannot be avoided in computation or experiment. This leads to a more general formulation in terms of symbolic dynamics and to the idea of weak universality. The connection is made with Turing's ideas of computable numbers and it is explained why the continuum approach leads to predictions that are not necessarily realized in computation or in nature, whereas the discrete approach yields all possible histograms that can be observed or computed.

Deterministic chaos. --- Algorithms. --- Mappings (Mathematics) --- Fractals. --- Mathematical physics. --- Physical mathematics --- Physics --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology) --- Maps (Mathematics) --- Functions --- Functions, Continuous --- Topology --- Transformations (Mathematics) --- Algorism --- Algebra --- Arithmetic --- Chaos, Deterministic --- Deterministic chaotic systems --- Chaotic behavior in systems --- Determinism (Philosophy) --- Mathematics --- Foundations --- Deterministic chaos --- Algorithms --- Fractals --- Mathematical physics

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Chiffrement --- Codes secrets --- Correspondance secrète --- Cryptage --- Cryptanalyse --- Cryptanalysis --- Cryptografie --- Cryptographie --- Cryptography --- Cryptologie --- Cryptology --- Déchiffrement --- Décodage --- Décryptage --- Décryptement --- Fractales --- Fractals --- Geometry [Non-Euclidean ] --- Getaltheorie --- Géometrie non-euclidienne --- Lettres secrètes --- Meetkunde [Niet-euclidische ] --- Messages cryptographiques --- Nombres [Theorie des ] --- Number theory --- Secret codes --- Secret writing --- Steganography --- Stéganographie --- Écriture cryptographique --- Écriture secrète --- Geometry, Non-Euclidean --- Géométrie non-euclidienne --- Théorie des nombres --- Geometry, Non-Euclidean. --- Number theory. --- Fractals. --- Cryptography. --- Géométrie non-euclidienne --- Théorie des nombres --- Number study --- Numbers, Theory of --- Algebra --- Non-Euclidean geometry --- Geometry --- Parallels (Geometry) --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology) --- Signs and symbols --- Symbolism --- Writing --- Ciphers --- Data encryption (Computer science) --- Foundations --- Geometry, Non-Euclidian. --- Number Theory --- Mathematiques --- Geometrie classique --- Arithmetique --- Vulgarisation