In this paper, we consider a one-parameter family Fλ of continuous maps on ℝm or ℝm × ℝk with the singular map F0 having one of the forms (i) F0(x) = f(x), (ii) F0(x, y) = (f(x), g(x)), where g : ℝm → ℝk is continuous, and (iii) F 0(x, y) = (f(x), g(x, y)), where g : ℝm × ℝk → ℝk is continuous and locally trapping along the second variable y. We show that if f : ℝm → ℝm is a C1 diffeomorphism having a topologically crossing homoclinic point, then Fλ has positive topological entropy for all λ close enough to 0.
- Multidimensional perturbation
- Topological crossing
- Topological entropy