Newhouse Laminations

2018/11/01 by Benedicks, Michael, Martens, Marco, Palmisano, Liviana
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1811.00617

Abstract

Newhouse laminations occur in unfoldings of rank-one homoclinic tangencies. Namely, in these unfoldings, there exist codimension 2 laminations of maps with infinitely many sinks which move simultaneously along the leaves. As consequence, in the space of real polynomial maps, there are examples of: Hénon maps, in any dimension, with infinitely many sinks, quadratic Hénon-like maps with infinitely many sinks and a period doubling attractor, quadratic Hénon-like maps with infinitely many sinks and a strange attractor, non trivial analytic families of polynomial maps with infinitely many sinks.

Related

• Newhouse Laminations of polynomials on ℂ²
• Coexistence of non-periodic attractors
• Existence of generic cubic homoclinic tangencies for Hénon maps
• Persistent homoclinic tangencies and infinitely many sinks for residual sets of automorphisms of low degree in C³
• On the classification of laminations associated to quadratic polynomials