Quantification géométrique et réduction symplectique
Quantitative recurrence in two-dimensional extended processes
Under some mild condition, a random walk in the plane is recurrent. In particular each trajectory is dense, and a natural question is how much time one needs to approach a given small neighbourhood of the origin. We address this question in the case of some extended dynamical systems similar to planar random walks, including ℤ2-extension of mixing subshifts of finite type. We define a pointwise recurrence rate and relate it to the dimension of the process, and establish a result of convergence in...
Quantization Dimension Function and Ergodic Measure with Bounded Distortion
The quantization dimension function for the image measure of a shift-invariant ergodic measure with bounded distortion on a self-conformal set is determined, and its relationship to the temperature function of the thermodynamic formalism arising in multifractal analysis is established.
Quantization of the orientation preserving automorphisms of the torus
Quantum cohomology of flag manifolds and quantum Toda lattices.
Quantum curve in -oscillator model.
Quantum deformations and superintegrable motions on spaces with variable curvature.
Quantum dynamical entropy and an algorithm by Gene Golub.
Quantum integrable systems
Quantum relativistic Toda chain.
Quantum super-integrable systems as exactly solvable models.
Quasiclassical limit of KP hierarchy, -symmetries, and free fermions
Quasi-compactness and mean ergodicity for Markov kernels acting on weighted supremum normed spaces
Let P be a Markov kernel on a measurable space E with countably generated σ-algebra, let w:E→[1, +∞[ such that Pw≤Cw with C≥0, and let be the space of measurable functions onE satisfying ‖f‖w=sup{w(x)−1|f(x)|, x∈E}<+∞. We prove that Pis quasi-compact on if and only if, for all , contains a subsequence converging in toΠf=∑di=1μi(f)vi, where the vi’s are non-negative bounded measurable functions on E and the μi’s are probability distributions on E. In particular, when the space of...
Quasiconformality in the Geodesic Flow of Negatively Curved Manifolds.
Quasigauge spaces with generalized quasipseudodistances and periodic points of dissipative set-valued dynamic systems.
Quasigraded Lie algebras and modified Toda field equations.
Quasi-linear algebras and integrability (the Heisenberg picture).
Quasilinear waves and trapping: Kerr-de Sitter space
In these notes, we will describe recent work on globally solving quasilinear wave equations in the presence of trapped rays, on Kerr-de Sitter space, and obtaining the asymptotic behavior of solutions. For the associated linear problem without trapping, one would consider a global, non-elliptic, Fredholm framework; in the presence of trapping the same framework is available for spaces of growing functions only. In order to solve the quasilinear problem we thus combine these frameworks with the normally...
Quasi-morphismes et invariant de Calabi
Quasi-periodic and periodic solutions of the Toda lattice via the hyperelliptic sigma function
A lattice model with exponential interaction, was proposed and integrated by M. Toda in the 1960s; it was then extensively studied as one of the completely integrable (differential-difference) equations by algebro-geometric methods, which produced both quasi-periodic solutions in terms of theta functions of hyperelliptic curves and periodic solutions defined on suitable Jacobians by the Lax-pair method. In this work, we revisit Toda’s original approach to give solutions of the Toda lattice in terms...