11 citations · 46 across the 25 of their papers we have counts for
35 papers
Emergence in dynamical systems
Pierre Berger
In [Be17], we introduced the notion of emergence to quantify the statistical complexity of a dynamical system. Roughly speaking, emergence measures the number of probability measur…
Generators of groups of Hamitonian maps
Pierre Berger, Dmitry Turaev
We prove that analytic Hamiltonian dynamics on tori, annuli, or Euclidean space can be approximated by a composition of nonlinear shear maps where each of the shears depends only o…
Parametric linearization of skew products
Pierre Berger, Bernhard Reinke
We establish a linearization criterion for skew products of contractions in any dimension. We prove their smooth or holomorphic parameter dependence. In the smooth setting, we use…
Every diffeomorphism is a total renormalization of a close to identity map
Pierre Berger, Nicolaz Gourmelon, Mathieu Helfter
For any , we show that every diffeomorphism of a manifold of the form is a total renormalization of a -close to identity map…
Analytic pseudo-rotations
Pierre Berger
We construct analytic symplectomorphisms of the cylinder or the sphere with zero or exactly two periodic points and which are not conjugated to a rotation. In the case of the cylin…
Steady Euler flows on with wild and universal dynamics
Pierre Berger, Anna Florio, Daniel Peralta-Salas
Understanding complexity in fluid mechanics is a major problem that has attracted the attention of physicists and mathematicians during the last decades. Using the concept of renor…