Orbits of homogeneous polynomials on Banach spaces

CARDECCIA, RODRIGO; MURO, SANTIAGO

ERGODIC THEORY AND DYNAMICAL SYSTEMS

CAMBRIDGE UNIV PRESS

Año: 2020 p. 1 - 29

0143-3857

We study the dynamics induced by homogeneous polynomials on Banach spaces. It is known that no homogeneous polynomial defined on a Banach space can have a dense orbit. We show a simple and natural example of a homogeneous polynomial with an orbit that is at the same time delta-dense (the orbit meets every ball of radius delta ), weakly dense and such that Gamma*Orb_P is dense for every Gamma contained in C that either is unbounded or has 0 as an accumulation point. Moreover, we generalize the construction to arbitrary infinite-dimensional separable Banach spaces. To prove this, we study Julia sets of homogeneous polynomials on Banach spaces.