Linear response, or else

Viviane Baladi (1) , Michael Benedicks (2) , Daniel Schnellmann (1)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 Mathematics KTH

Consider a smooth one-parameter family t -> f_t of dynamical systems f_t, with |t| m_t is differentiable at t=0 (possibly in the sense of Whitney), and if its derivative can be expressed as a function of f_0, m_0, and d_t f_t|_(t=0). The goal of this note is to present to a general mathematical audience recent results and open problems in the theory of linear response for chaotic dynamical systems, possibly with bifurcations.

Mots clés: Hyperbolic dynamical systems; Linear response; Transfer operator; Ruelle operator; Physical measure; SRB measure; Bifurcations; Differentiable dynamical system; Unimodal maps; Expanding interval maps

Domaines: Systèmes dynamiques [math.DS]

Viviane Baladi, Michael Benedicks, Daniel Schnellmann. Linear response, or else. 2014. ⟨hal-01055902⟩