Abstract
Abstract
It is well known that a family of tent-like maps with bounded derivatives has no linear response for typical deterministic perturbations changing the value of the turning point. In this note we prove the following result: if we consider a tent-like family with a cusp at the turning point, we recover the linear response. More precisely, let T
ɛ
be a family of such cusp maps generated by changing the value of the turning point of T
0 by a deterministic perturbation and let h
ɛ
be the corresponding invariant density. We prove that
ε
↦
h
ε
is differentiable in L
1 and provide a formula for its derivative.
Funder
Ministero dell’Istruzione, dell’Università e della Ricerca
Engineering and Physical Sciences Research Council