Title: Coexistence of invariant sets with and without SRB measures in Henon family
Authors: Kiriki, Shin
Li, Ming-Chia
Soma, Teruhiko
Department of Applied Mathematics
Issue Date: 1-Sep-2010
Abstract: Let {f(a,b)} be the (original) Henon family. In this paper, we show that, for any b near 0, there exists a closed interval J(b) which contains a dense subset J' such that, for any a is an element of J', f(a,b) has a quadratic homoclinic tangency associated with a saddle fixed point of f(a,b) which unfolds generically with respect to the one-parameter family {f(a,b)}(a is an element of Jb). By applying this result, we prove that J(b) contains a residual subset A(b)((2)) such that, for any a is an element of A(n)((2)), f(a,b) admits the Newhouse phenomenon. Moreover, the interval Jb contains a dense subset (A) over tilde (b) such that, for any a is an element of (A) over tilde (b), f(a,b) has a large homoclinic set without SRB measure and a small strange attractor with SRB measure simultaneously.
URI: http://dx.doi.org/10.1088/0951-7715/23/9/010
ISSN: 0951-7715
DOI: 10.1088/0951-7715/23/9/010
Volume: 23
Issue: 9
Begin Page: 2253
End Page: 2269
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