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Sequences of Filtrations

  • Michael Shub

Abstract

Let M: Ø=M 0 ⊂ ··· ⊂ M k , = M and N: Ø=N 0 ⊂ ··· ⊂ N l = M be two filtrations of M. We say that N refines M if and only if for all i = 0,..., l − 1, there is a j, 0 ≤ jk − 1 such that (N i +1N i ) ⊂ (M j +1M j ).

Keywords

Vector Field Lyapunov Function Disjoint Union Global Stability Catastrophe Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [3.1]
    Pugh, C. C. and Shub, M., a-stability theorem for flows, Invent. Math. 11 (1970), 150.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [3.2]
    Wilson, F. W., Smoothing derivatives of functions and applications, Trans. Amer. Math. Soc. 139 (1969), 413.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Michael Shub
    • 1
  1. 1.Thomas J. Watson Research CenterIBMYorktown HeightsUSA

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