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Standard texts and research in economics and finance ignore the absence of evidence from the analysis of real, unmassaged market data to support the notion of Adam Smith's stabilizing Invisible Hand. The neo-classical equilibrium model forms the theoretical basis for the positions of the US Treasury, the World Bank and the European Union, accepting it as their credo. It provides the theoretical underpinning for globalization, expecting to achieve the best of all possible worlds via the deregulation of all markets. In stark contrast, this text introduces a empirically based model of financial market dynamics that explains volatility, prices options correctly and clarifies the instability of financial markets. The emphasis is on understanding how real markets behave, not how they hypothetically 'should' behave. This text is written for physics graduate students and finance specialists, but will also serve as a valuable resource for those with a less mathematical background.

Finance --- Business mathematics --- Statistical physics --- Finances --- Mathématiques financières --- Physique statistique --- Mathematical models --- Statistical methods --- Modèles mathématiques --- Méthodes statistiques --- Business mathematics. --- Markets --- Statistical physics. --- Mathematical models. --- Statistical methods. --- AA / International- internationaal --- 305.91 --- 333.605 --- Econometrie van de financiële activa. Portfolio allocation en management. CAPM. Bubbles. --- Nieuwe financiële instrumenten. --- Mathématiques financières --- Modèles mathématiques --- Méthodes statistiques --- Physics --- Mathematical statistics --- Public markets --- Commerce --- Fairs --- Market towns --- Arithmetic, Commercial --- Business --- Business arithmetic --- Business math --- Commercial arithmetic --- Mathematics --- Econometrie van de financiële activa. Portfolio allocation en management. CAPM. Bubbles --- Nieuwe financiële instrumenten --- General and Others --- Econophysics. --- Economics

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Deterministic chaos --- Algorithms --- Mappings (Mathematics) --- Fractals --- Mathematical physics --- Chaos in systems --- Chaotic behavior in systems --- Chaotic motion in systems --- Chaotisch gedrag in de systemen --- Comportement chaotique dans les systèmes --- Differentiable dynamical systems --- Differentieerbare dynamicasystemen --- Fractales --- Systèmes dynamiques différentiables --- Differential geometry. Global analysis --- Algorithmes --- Chaos déterministe --- Applications (Mathématiques) --- Physique mathématique --- Algorithms. --- Deterministic chaos. --- Fractals. --- Mappings (Mathematics). --- Mathematical physics. --- Chaos déterministe --- Applications (mathématiques) --- #TELE:MI2 --- Physical mathematics --- Physics --- Maps (Mathematics) --- Functions --- Functions, Continuous --- Topology --- Transformations (Mathematics) --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology) --- Chaos, Deterministic --- Deterministic chaotic systems --- Determinism (Philosophy) --- Algorism --- Algebra --- Arithmetic --- Mathematics --- Foundations --- #TELE:SISTA --- Chaos déterministe. --- Algorithmes. --- Fractales. --- Chaos déterministe. --- Applications (mathématiques)

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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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