Sequences of Filtrations

  • Michael Shub


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 ).


Vector Field Lyapunov Function Disjoint Union Global Stability Catastrophe Theory 
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  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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