7 papers
Convergent realizations of Lie subalgebras
Karine Beauchard, Jérémy Le Borgne, Jérémy Le Borgne +2
It has been known since the seminal work of Guillemin and Sternberg that Lie subalgebras of finite codimension of an arbitrary real or complex Lie algebra can be realized as subalg…
Local convergence of Sussmann's infinite product for analytic vector fields
Jérémy Le Borgne, Frédéric Marbach
In 1986, Sussmann proposed an expansion of the Chen series as an infinite product of exponentials of Hall basis elements multiplied by coefficients defined through a simple inducti…
Small-time local control of a Schrödinger equation: a negative and a positive quadratic result
Karine Beauchard, Frédéric Marbach, Thomas Perrin
We study the small-time local controllability (STLC) of a bilinear Schrödinger equation with Neumann boundary conditions near its ground state. We focus on the degenerate case whe…
Control theory and splitting methods
Karine Beauchard, Adrien Busnot Laurent, Frédéric Marbach
Our goal is to highlight some deep connections between numerical splitting methods and control theory. We consider evolution equations of the form , wher…
Time-iteration methods for controllability
Frédéric Marbach
These notes are based on a short course delivered at the Summer School EUR MINT 2025 "Control, Inverse Problems and Spectral Theory", held in June 2025 in Toulouse, France. The cou…
Nonlinear Forward-Backward Problems
Anne-Laure Dalibard, Frédéric Marbach, Jean Rax
We prove the existence and uniqueness of strong solutions to the equation in the vicinity of the linear shear flow, subject to perturbations of the source term…