$C^2$-robust heterodimensional tangencies
  In this paper, we give sufficient conditions for the existence of $C^{2}$ robust heterodimensional tangency, and present a nonempty open set in $\Diff^2(M)$ with $\dim(M)\geq 3$ each element of which has a non-degenerate heterodimensional tangency on a $C^2$ robust heterodimensional cycle. 
Shin Kiriki and Teruhiko Soma
math.DS nlin.CD