On the Dynamics of $n$-Dimensional Quadratic Endomorphisms

Abstract:

Considering a convex endomorphism F (its n coordinates are convex functions) and the one parameter family F _μ=F−μν, where ν is any vector of ℝⁿ, we find sufficient conditions in order that for large values of the parameter, the dynamical behavior of F _μ is completely described: either the nonwandering set Ω(F _μ) is empty or F _μ restricted to Ω(F _μ) is an expanding map. These conditions are shown to be generic in the space of quadratic endomorphisms.