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Computer-assisted proofs in analysis. (English) Zbl 0599.58036
Computers have a number of uses in mathematics and mathematical physics. Two which are relatively familiar are heuristic numerical exploration and determining properties of discrete objects (e.g., testing integers for primality). We describe here an example of a less familiar use of computers: the strict verification of estimates on continuously variable quantities (real numbers) for use in the proof of qualitative statements in analysis.

MSC:
37G99 Local and nonlocal bifurcation theory for dynamical systems
65-04 Software, source code, etc. for problems pertaining to numerical analysis
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References:
[1] Collet, P; Eckmann, JP, Iterated maps on the interval as dynamical systems, (1980), Birkhäuser
[2] Lanford, OE, A computer-assisted proof of the Feigenbaum conjectures, Bull. A.M.S., 6, 427-434, (1982), (New Series) · Zbl 0487.58017
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