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2000•Dynamics and Stability of SystemsRequires access

An isolated saddle-node bifurcation occurring inside a horseshoe

Yongluo Cao, Shin Kiriki

Open publisher page 8 citations

Abstract

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

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What this paper is about

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

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OpenAlex reports 8 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

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

Key concepts: Saddle-node bifurcation, Bifurcation, Mathematics, Horseshoe (symbol), Invariant (physics), Saddle, Bifurcation diagram, Mathematical analysis

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