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 ≤ j ≤ k − 1 such that (N i +1 − N i ) ⊂ (M j +1 − M j ).
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References
Pugh, C. C. and Shub, M., a-stability theorem for flows, Invent. Math. 11 (1970), 150.
Wilson, F. W., Smoothing derivatives of functions and applications, Trans. Amer. Math. Soc. 139 (1969), 413.
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© 1987 Springer-Verlag Berlin Heidelberg
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Shub, M. (1987). Sequences of Filtrations. In: Global Stability of Dynamical Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-1947-5_3
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DOI: https://doi.org/10.1007/978-1-4757-1947-5_3
Publisher Name: Springer, New York, NY
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