Browsing by Author "Kiriki, Shin"

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Coexistence of invariant sets with and without SRB measures in Henon family
(2010-09-01)
Kiriki, Shin
;
Li, Ming-Chia
;
Soma, Teruhiko
;
應用數學系
;
Department of Applied Mathematics
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.
GEOMETRIC LORENZ FLOWS WITH HISTORIC BEHAVIOR
(2016-12)
Kiriki, Shin
;
Li, Ming-Chia
;
Soma, Teruhiko
;
應用數學系
;
Department of Applied Mathematics
We will show that, in the the geometric Lorenz flow, the set of initial states which give rise to orbits with historic behavior is residual in a trapping region.