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Shin Kiriki

Publications and source records attributed to Shin Kiriki.

22 records · Page 2Linked to original sources
arXiv2009

Heterodimensional tangencies on cycles leading to strange attractors

In this paper, we study heterodimensional cycles of two-parameter families of 3-dimensional diffeomorphisms some element of which contains nondegenerate heterodimensional tangencies of the stable and unstable manifolds of two saddle points with different indexes, and prove that such diffeomorphisms can be well approximated by another element which has a quadratic homoclinic tangency associated to one of these saddle points. Moreover, it is shown that the tangency unfolds generically with respect to the family. This result together with some theorem in Viana, we detect strange attractors appeared arbitrarily close to the original element with the heterodimensional cycle.

math.DS↗
arXiv2008

Persistent antimonotonic bifurcations and strange attractors for cubic homoclinic tangencies

In this paper, we study a two-parameter family of two-dimensional diffeomorphisms such that it has a cubic homoclinic tangency unfolding generically which is associated with a dissipative saddle point. Our first theorem presents an open set in the parameter-plane such that, for any parameter value in the open set, there exists a one-parameter subfamily through this value exhibiting cubically related persistent contact-making and contact-breaking quadratic tangencies. Moreover, the second theorem shows that any such two-parameter family satisfies Wang-Young's conditions which guarantee that it exhibits a cubic polynomial-like strange attractor with an SRB measure.

math.DS↗
arXiv1998

The isolated saddle-node bifurcation occurring inside a horseshoe

In this paper, we consider a smooth arc of diffeomorphisms which has a saddle-node bifurcation inside a nontrivial invariant set which is a deformation of a horseshoe. We show that this saddle-node bifurcation is isolated, that is, its hyperbolicity is maintained before and after the saddle-node bifurcation. Moreover we construct a $C^2$-open set of arcs having the same property.

math.DS↗