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GEVREY SERIES AND DYNAMIC BIFURCATIONS FOR ANALYTIC SLOW-FAST MAPPINGS
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UNSPECIFIED (1995) GEVREY SERIES AND DYNAMIC BIFURCATIONS FOR ANALYTIC SLOW-FAST MAPPINGS. NONLINEARITY, 8 (2). pp. 179-201. ISSN 0951-7715.
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Abstract
The surprising effects of slow sweep of a parameter in a family of dynamical systems exhibiting bifurcations are known as dynamic bifurcations. In this paper we study dynamic bifurcations in the context of analytic slow-fast mappings of the form F-v(x, lambda)=(f(x, lambda), lambda z + v) for small v in the neighbourhood of an analytic curve x = y(lambda) of fixed points of f(., lambda).
Firstly, we construct a formal power series expansion U in powers of v for invariant curves lambda --> U(lambda, v) close to the curve of fixed points, and prove it is Gevrey-l, Secondly we show how the behaviour of the orbits, and in particular the existence of a delay for the dynamic bifurcation, can be derived as a direct consequence of the analytical properties of this formal series.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Journal or Publication Title: | NONLINEARITY | ||||
Publisher: | IOP PUBLISHING LTD | ||||
ISSN: | 0951-7715 | ||||
Official Date: | March 1995 | ||||
Dates: |
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Volume: | 8 | ||||
Number: | 2 | ||||
Number of Pages: | 23 | ||||
Page Range: | pp. 179-201 | ||||
Publication Status: | Published |
Data sourced from Thomson Reuters' Web of Knowledge
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