论文标题
同型斜角切线的两参数展开的强大异量级循环
Robust heterodimensional cycles in two-parameter unfolding of homoclinic tangencies
论文作者
论文摘要
我们考虑$ c^r $ $（r = 3，\ dots，\ infty，ω）$ diffemorithism，具有通用的同型固定性，与双曲线周期性点具有通用的同型截面，在该点上，这个点至少具有一个（非真实的）中心乘数，并且对中心的多与中心的某些明确的假设在中心上很满意，使得动态既不是在官能上的固定性，而是有效的。我们证明，$ c^1 $ - 抛光的杂二量周期在任何通用的两参数$ c^r $ $ $上都出现在这种切实的情况下。这些异量级循环也具有$ C^1 $ - 固定的同层次切线。
We consider $C^r$ $(r=3,\dots,\infty,ω)$ diffeomorphisms with a generic homoclinic tangency to a hyperbolic periodic point, where this point has at least one complex (non-real) central multiplier and some explicit assumptions on central multipliers are satisfied so that the dynamics near the homoclinic tangency is not effectively one-dimensional. We prove that $C^1$-robust heterodimensional cycles of co-index one appear in any generic two-parameter $C^r$-unfolding of such a tangency. These heterodimensional cycles also have $C^1$-robust homoclinic tangencies.
