Tootfinder

Almost reducibility, distortion and local perfection for diffeomorphisms of one-manifolds
H\'el\`ene Eynard-Bontemps (IF, IMJ-PRG), Emmanuel Militon (LJAD, UniCA)
https://arxiv.org/abs/2507.13770

Almost reducibility, distortion and local perfection for diffeomorphisms of one-manifolds
In this article, we characterize the distortion elements of the group of smooth diffeomorphisms of the circle and of the group of compactly supported smooth diffeomorphisms of the real line. More precisely, we prove that, in this context, an element is distorted if and only if it is almost reducible, that is if and only if it has conjugates arbitrarily close to an isometry. For diffeomorphisms with fixed points, we show that this is equivalent to being the time-1 map of a C 1 vector field witho…

Von #MichaelElsener @michaelelsener@instagram.com
So absurd komisch definiert Christoph #Blocher „Neutralität“ in seinem Vortrag. 😂 Was fällt dir noch für ein tolles Adjektiv ein für unsere #Neutralität

Leaked all-hands: Mathias Döpfner said Axel Springer employees must use AI, opposed disclosing to readers whether AI was used in the reporting process, and more (Oliver Darcy/Status)
https://www.status.news/p/axel-springer-mathias-dopfner-ai-policy

Axel Springer’s A.I. Edict
At a global town hall, Axel Springer boss Mathias Döpfner delivered a blunt message—A.I. is here, and every employee must use it.

Expansive Natural Neural Gradient Flows for Energy Minimization
Wolfgang Dahmen, Wuchen Li, Yuankai Teng, Zhu Wang
https://arxiv.org/abs/2507.13475 https:/…

Expansive Natural Neural Gradient Flows for Energy Minimization
This paper develops expansive gradient dynamics in deep neural network-induced mapping spaces. Specifically, we generate tools and concepts for minimizing a class of energy functionals in an abstract Hilbert space setting covering a wide scope of applications such as PDEs-based inverse problems and supervised learning. The approach hinges on a Hilbert space metric in the full diffeomorphism mapping space, which could be viewed as a generalized Wasserstein-2 metric. We then study a projection gr…

Positive curvature conditions on contractible manifolds
Paul Sweeney Jr
https://arxiv.org/abs/2507.15719 https://arxiv.org/pdf/2507.1…

Positive curvature conditions on contractible manifolds
Our goal is to identify curvature conditions that distinguish Euclidean space in the case of open, contractible manifolds and the disk in the case of compact, contractible manifolds with boundary. First, we show that an open manifold that is the interior of a sufficiently connected, compact, contractible 5-manifold with boundary and supports a complete Riemannian metric with uniformly positive scalar curvature is diffeomorphic to Euclidean 5-space. Next, we investigate the analogous question fo…

Die ePetition 183103 an den Bundestag aus dem Bereich Telekommunikationsgesetz (TKG) mit dem Titel
Anrufsperre für beliebig definierte Rufnummern(teil)bereiche
kann bis zum Mittwoch 01. Oktober 2025 01:00 UTC mitgezeichnet werden und lautet
Mit der Petition wird eine gesetzliche Verpflichtung f…

Die ePetition 183103 an den Bundestag aus dem Bereich Telekommunikationsgesetz (TKG) mit dem Titel
Anrufsperre für beliebig definierte Rufnummern(teil)bereiche
kann bis zum Mittwoch 01. Oktober 2025 01:00 UTC mitgezeichnet werden und lautet
Mit der Petition wird eine gesetzliche Verpflichtung f…

Geometric, topological and dynamical properties of conformally symplectic systems, normally hyperbolic invariant manifolds, and scattering maps
Marian Gidea, Rafael de la Llave, Tere M-Seara
https://arxiv.org/abs/2508.14794

Geometric, topological and dynamical properties of conformally symplectic systems, normally hyperbolic invariant manifolds, and scattering maps
Conformally symplectic diffeomorphisms $f:M \rightarrow M$ transform a symplectic form $ω$ on a manifold $M$ into a multiple of itself, $f^* ω= ηω$. We assume $ω$ is bounded, as some of the results may fail otherwise. We show that there are deep interactions between the topological properties of the manifold, the dynamical properties of the map, and the geometry of invariant manifolds. We show that, when the symplectic form is not exact, the possible conformal factors $η$ are related …