A classification of explosions in dimension one
2009 ◽
Vol 29
(2)
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pp. 715-731
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Keyword(s):
AbstractA discontinuous change in the size of an attractor is the most easily observed type of global bifurcation. More generally, anexplosionis a discontinuous change in the set of recurrent points. An explosion often results from heteroclinic and homoclinic tangency bifurcations. We prove that, for one-dimensional maps, explosions are generically the result of either tangency or saddle-node bifurcations. Furthermore, we give necessary and sufficient conditions for generic tangency bifurcations to lead to explosions.
2003 ◽
Vol 35
(04)
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pp. 1111-1130
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2002 ◽
Vol 12
(04)
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pp. 709-737
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2004 ◽
Vol 134
(6)
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pp. 1177-1197
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2020 ◽
Vol ahead-of-print
(ahead-of-print)
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1988 ◽
Vol 93
(2)
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pp. 279-293
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2002 ◽
Vol 131
(1)
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pp. 219-229
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1995 ◽
Vol 129
(3)
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pp. 225-244
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