Superdiffusive limits for deterministic fast-slow dynamical systems.

We consider deterministic fast-slow dynamical systems on R m × Y of the form x k + 1 ( n ) = x k ( n ) + n - 1 a ( x k ( n ) ) + n - 1 / α b ( x k ( n ) ) v ( y k ) , y k + 1 = f ( y k ) , where α ∈ ( 1 , 2 ) . Under certain assumptions we prove convergence of the m-dimensional process X n ( t ) = x ⌊ n t ⌋ ( n ) to the solution of the stochastic differential equation d X = a ( X ) d t + b ( X ) ⋄ d L α , where L α is an α -stable Lévy process and ⋄ indicates that the stochastic integral is in the Marcus sense. In addition, we show that our assumptions are satisfied for intermittent maps f of Pomeau-Manneville type.