Celebratio Mathematica — Williams — Complete Bibliography

Complete Bibliography

Works connected to François Ledrappier

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R. F. Williams: “Spaces that won’t say no,” pp. 236–246 in International conference on dynamical systems (Montivideo, Uruguay, 27 March–1 April 1995). Edited by F. Ledrappier, J. Lewowicz, and S. Newhouse. Pitman Research Notes in Mathematics 362. Longman Scientific & Technical (Harlow, UK), 1996. Proceedings dedicated to Ricardo Mañé. MR 1460809 Zbl 0876.57044 incollection

A class of spaces \( K \) and their natural maps \[ f:K\to K^{\prime} \] were introduced in [Williams 1974] which satisfies the defining property that \[ f_*:H_n(K) \to H_n(K^{\prime}) \] is always a “positive matrix”. Here \( n \) is the dimension of both \( K \) and \( K^{\prime} \); we follow the usage in symbolic dynamics and say that a matrix is positive provided all its entries are \( \geq 0 \). The purpose of this paper is to show how a natural construction related to the “DA” maps of Smale [Williams 1970] often leads to SOB’s and in particular shows that they exist in all dimensions. Here we present the easier conceptual parts of this theory and elicit a geometric property which when it holds leads to quite satisfactory proofs.

Ricardo Mañé	Related
Sheldon Earle Newhouse	Related
François Ledrappier	Related
Jorge Lewowicz	Related