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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Explosions in completely unstable flows. II. Some examples


Author: Zbigniew Nitecki
Journal: Trans. Amer. Math. Soc. 245 (1978), 63-88
MSC: Primary 58F10
MathSciNet review: 511400
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Abstract: A dynamical system with all points wandering is ``explosive'' if some $ {C^0}$ perturbation has nonwandering points. It is known that the plane admits no explosive cascades or flows; in this paper, examples are constructed to show that all open manifolds except $ {R^1}$ and $ {R^2}$ admit explosive flows (and hence cascades).


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DOI: https://doi.org/10.1090/S0002-9947-1978-0511400-6
Keywords: Completely unstable flow, $ \Omega $-explosion, open manifold
Article copyright: © Copyright 1978 American Mathematical Society