## Domains for Computation in Mathematics, Physics and Exact Real Arithmetic (1997)

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Venue: | Bulletin of Symbolic Logic |

Citations: | 49 - 10 self |

### BibTeX

@ARTICLE{Edalat97domainsfor,

author = {Abbas Edalat},

title = {Domains for Computation in Mathematics, Physics and Exact Real Arithmetic},

journal = {Bulletin of Symbolic Logic},

year = {1997},

volume = {3},

pages = {401--452}

}

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### Abstract

We present a survey of the recent applications of continuous domains for providing simple computational models for classical spaces in mathematics including the real line, countably based locally compact spaces, complete separable metric spaces, separable Banach spaces and spaces of probability distributions. It is shown how these models have a logical and effective presentation and how they are used to give a computational framework in several areas in mathematics and physics. These include fractal geometry, where new results on existence and uniqueness of attractors and invariant distributions have been obtained, measure and integration theory, where a generalization of the Riemann theory of integration has been developed, and real arithmetic, where a feasible setting for exact computer arithmetic has been formulated. We give a number of algorithms for computation in the theory of iterated function systems with applications in statistical physics and in period doubling route to chao...

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Citation Context ..., for any pair of non-empty open sets a, b # X , there exists n > 0 such that f n (a) # b #= #, and (ii) the periodic points of f are dense in X . If X is in fact a metric space, then it can be shown =-=[5]-=- that a chaotic map is sensitive to initial conditions i.e., there exists # > 0 such that, for any x # X and any neighbourhood N of x, there exists y # N and n # 0 such that d (f n (x), f n (y)) > #. ... |

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