4 papers
Multiple recurrence and hypercyclicity
Rodrigo Cardeccia, Santiago Muro
We study multiply recurrent and hypercyclic operators as a special case of -hypercyclicity, where is the family of subsets of the natural numbers containin…
Arithmetic progressions and chaos in linear dynamics
Rodrigo Cardeccia, Santiago Muro
We characterize chaotic linear operators on reflexive Banach spaces in terms of the existence of long arithmetic progressions in the sets of return times. To achieve this, we study…
Hypercyclic bilinear operators on Banach spaces
Rodrigo Cardeccia
We study the dynamics induced by an -linear operator. We answer a question of Bès and Conejero showing an example of an -linear hypercyclic operator acting on a Banach space.…
Orbits of homogeneous polynomials on Banach spaces
Rodrigo Cardeccia, Santiago Muro
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 s…