Decidability of chaos for some families of dynamical systems

Carlos Matheus | Arbieto, Alexander

Keywords: Decidability | Chaos | Lyapunov exponents | SRB measues | topological entropy.

We show that positive Lyapounov exponents and existence of SRB measures for some parametrized families of interesting dynamical systems (quadra-tic family and Hénon maps) are not decidable sets in the parameter space. Because the existence of positive exponents (or SRB measures) is, in a natural way, associated to chaos, these results go in the direction of a conjecture by Smale and Carleson: ``Chaos is not decidable''.

Anexos:

• decid_chaos_full.pdf