Abstract: I will talk about some technical topics from the paper arXiv:1808.07218.

(see https://arxiv.org/abs/1808.07218 )

Given a partially hyperbolic heterodimensional cycle, by adding $C^r$-small perturbation nearby, one

can create degenerate periodic points. I explain some ingredients of such construction, including Takens

coordinates and the calculation techniques of compositions of germs of polynomials.