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Research
4,454+ open-access research outputs.
In this note we survey some of our results on the Lagrangian reduction of discrete-time mechanical systems (DMSs). It is intended as an introduction to the general ideas that we used in the reduction …
An involutive link is a link which is invariant under the standard rotation by 180 degrees in $S^3$. We establish an equivariant analogue of the work of Carter and Saito aimed at studying equivariant …
The notion of \emph{concurrence} was recently proposed as the natural compatibility relation between Dirac structures, generalizing the commutativity of two Poisson structures. We address the question…
We give a simple description of the coordinate ring of the universal centralizer associated to a simply connected semisimple group. To this end, we prove a general result on Weil restriction of affine…
Let $\bar{S}_2$ be the Lie algebra of polynomial vector fields on $A_2=\mathbb{C}[t_1,t_2]$ with constant divergence.In this paper, we first show that each block $\Omega^{\widetilde{S}_2}_{\mathbf{a}}…
We show that closed surfaces with minimal total absolute curvature in Cartan-Hadamard 3-manifolds bound flat convex bodies. This generalizes Chern-Lashof's theorem for surfaces in Euclidean space and …
We study the resonance spectrum of the multiflow induced on a flag manifold by the action, through multiplication by the exponential map, of the Cartan subalgebra of the underlying Lie group. We give …
Let $A:=\mathbb{C}[z_+,z_-]\otimes \Lambda(\theta_1,\theta_2,\theta_3)$, with $z_\pm$ even and $\theta_1,\theta_2,\theta_3$ odd. For a reductive Lie algebra $\mathfrak g$, let $\mathfrak g[A]:=\mathfr…
A finite Euclidean set is diameter-Ramsey if, for every number of colors, some finite same-diameter witness has the property that every coloring of the witness contains a monochromatic congruent copy …
We investigate the competition between two distinct mechanisms generating stable laws in deterministic dynamical systems: slow mixing of the system and heavy-tailed observables. For heavy-tailed obs…
Corsten and Frankl conjectured that a simplex is diameter-Ramsey if and only if its circumcenter lies in its convex hull. We disprove this conjecture in every dimension $d\ge 3$. The main tool is a su…
In this paper we prove existence and classification results for translating solitons defined as initial conditions for higher order mean curvature flows that are invariant by translations in warped pr…
This Part develops structural consequences of the thermodynamic formalism for Axiom A diffeomorphisms. The Pesin Entropy Formula equates the metric entropy of the SRB measure to the sum of positive Ly…
We establish statistical limit theorems for equilibrium states of Axiom A diffeomorphisms, derived from the spectral gap of the Ruelle transfer operator established in Part I (Thiam2026a) and transfer…
We study explicit conformal minimal immersions into $\mathbb{R}^5$ obtained from holomorphic null curves in $\mathbb{C}^5$. Although the general correspondence between conformal minimal immersions in …
We develop the convex-analytic structure of the thermodynamic formalism for continuous maps on compact metric spaces. The pressure functional is the Legendre-Fenchel transform of the negative entropy,…
We prove that five characterizations of Gibbs measures for H\"{o}lder potentials on topologically mixing subshifts of finite type are equivalent: the Jacobian condition, the classical cylinder-based G…
Furstenberg's flow on the infinite-dimensional torus $\mathbb{T}^\omega$ is defined by \[ T (x_1, x_2, \ldots, x_\nu, \ldots) = (x_1 + \alpha, x_2 + h(x_1), \ldots, x_\nu + h(x_1 + (\nu-2)\beta)…
The study of Sobolev and Poincar\'e inequalities for differential forms in Carnot groups and in the more general sub-Riemannian setting is still an open problem in its full generality. One may conject…
A criterion for proving a strong form of propagation of chaos on the path space, known as entropy chaos, for a general interacting diffusion system is proposed. Our analysis focuses on the class of co…
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