10 citations · 12 across the 4 of their papers we have counts for
7 papers
-robust homoclinic tangencies
Dongchen Li
The aim of this paper is twofold. First, we introduce standard blenders (special hyperbolic sets) and their variations, and prove their fundamental properties on the generation of…
Blender-producing mechanisms and a dichotomy for local dynamics for heterodimensional cycles
Dongchen Li
Blenders are special hyperbolic sets used to produce various robust dynamical phenomena which appear fragile at first glance. We prove for diffeomorphisms ($r=2,\dots,\infty,…
Robust heterodimensional cycles in two-parameter unfolding of homoclinic tangencies
Dongchen Li, Xiaolong Li, Katsutoshi Shinohara +1
We establish a necessary and sufficient condition for the birth of heterodimensional cycles from a generic homoclinic tangency to a hyperbolic periodic orbit. We prove for ($…
Persistence of Heterodimensional Cycles
Dongchen Li, Dmitry Turaev
A heterodimensional cycle is an invariant set of a dynamical system consisting of two hyperbolic periodic orbits with different dimensions of their unstable manifolds and a pair of…
Persistent heterodimensional cycles in periodic perturbations of Lorenz-like attractors
Dongchen Li, Dmitry Turaev
We prove that heterodimensional cycles can be created by unfolding a pair of homoclinic tangencies in a certain class of C-infinity diffeomorphisms. This implies the existence of a…
Homoclinic Bifurcations that Give Rise to Heterodimensional Cycles near A Saddle-Focus Equilibrium
Dongchen Li
We show that heterodimensional cycles can be born at the bifurcations of a pair of homoclinic loops to a saddle-focus equilibrium for flows in dimension 4 and higher. In addition t…