https://hdl.handle.net/2072/201036 2026-04-08T03:26:33Z 2026-04-08T03:26:33Z Balacheff, Florent Sardà, Teo Gil Moreno de Mora Sabourau, Stéphane https://hdl.handle.net/2072/489313 2026-03-10T10:20:39Z 2025-06-04T00:00:00Z

Complete 3-manifolds of positive scalar curvature with quadratic deca Balacheff, Florent; Sardà, Teo Gil Moreno de Mora; Sabourau, Stéphane We prove that if an orientable 3-manifold M admits a complete Riemannian mètric whose scalar curvature is positive and has a subquadratic decay at infinity, then it decomposes as a (possibly infinite) connected sum of spherical manifolds and S2×S1 summands. This generalises a theorem of Gromov andWang by using a different,more topological, approach. As a result, the manifold M carries a complete Riemannian metric of uniformly positive scalar curvature, which partially answers a conjecture of Gromov. More generally, the topological decomposition holds without any scalar curvature assumption under a weaker condition on the filling discs of closed curves in the universal cover based on the notion of fill radius. Moreover, the decay rate of the scalar curvature is optimal in this decomposition theorem. Indeed, the manifold R2×S1 supports a complete metric of positive scalar curvature with exactly quadràtic decay, but does not admit a decomposition as a connected sum.

2025-06-04T00:00:00Z Berk, P. Trujillo, Frank Wu, H. https://hdl.handle.net/2072/489312 2026-03-10T10:21:43Z 2025-06-11T00:00:00Z

Ergodic properties of infinite extension of symmetric interval exchange transformations Berk, P.; Trujillo, Frank; Wu, H. We prove that skew products with the co cycle given by the function f (x) = a(x-1/2) with a not equal 0 are ergodic for every ergodic symmetric IET in the base, thus giving the full characterization of ergodic extensions in this family. Moreover, we prove that under an additional natural assumption of unique ergodicity on the IET, we can replace f with any differentiable function with a non-zero sum of jumps. Finally, by considering weakly mixing IETs instead of just ergodic, we show that the skew products with co cycle given by f have infinite ergodic index.

2025-06-11T00:00:00Z Antonelli, V. Malaspina, F. Marchesi, Simone Pons-Llopis, J. https://hdl.handle.net/2072/489311 2026-03-10T10:21:09Z 2025-10-25T00:00:00Z

‘t Hooft bundles on the complete flag threefold and moduli spaces of instantons Antonelli, V.; Malaspina, F.; Marchesi, Simone; Pons-Llopis, J. In this work we study the moduli spaces of instanton bundles on the flag twistor space F := F (0, 1, 2). We stratify them in terms of the minimal twist supporting global sections and we introduce the notion of (special) 't Hooft bundle on F. In particular we prove that there exist mu -stable 't Hooft bundles for each admissible charge k. We completely describe the geometric structure of the moduli space of (special) 't Hooft bundles for arbitrary charge k. Along the way to reach these goals, we describe the possible structures of multiple curves supported on some rational curves in F as well as the family of del Pezzo surfaces realized as hyperplane sections of F. Finally we investigate the splitting behavior of 't Hooft bundles when restricted to conics.

2025-10-25T00:00:00Z Garrido, M. Martin, Pau Paradela, J. https://hdl.handle.net/2072/489310 2026-03-10T10:15:44Z 2025-06-23T00:00:00Z

Parabolic Saddles and Newhouse Domains in Celestial Mechanics Garrido, M.; Martin, Pau; Paradela, J. In McGehee (J Differ Equ 14:70–88, 1973) McGehee introduced a compactification of the phase space of the restricted 3-body problem by gluing a manifold of periodic orbits “at infinity”. Although from the dynamical point of view these periodic orbits are parabolic (the linearization of the Poincaré map is the identity matrix), one of them, denoted here by O, possesses stable and unstable manifolds which, moreover, separate the regions of bounded and unbounded motion. This observation prompted the investigation of the homoclinic picture associated to O, starting with the work of Alekseev (Uspehi Mat Nauk 23:209–210, 1968), Alekseev (Mat Sb 77(119):545–601, 1968) and Moser (Stable and random motions in dynamical systems. Princeton Landmarks in Mathematics. With special emphasis on celestial mechanics, Reprint of the 1973 original, With a foreword by Philip J. Holmes, 2001). We continue this research and extend, to this degenerate setting, some classical results in the theory of homoclinic bifurcations. More concretely, we prove that there exist Newhouse domainsN in parameter space (the ratio of masses of the bodies) and residual subsets R ⊂ N for which the homoclinic class of O has maximal Hausdorff dimension and is accumulated by generic elliptic periodic orbits. One of the main consequences of our work is the fact that, for a (locally) topologically large set of parameters of the restricted 3-body problem the union of its elliptic islands forms an unbounded subset of the phase space and, moreover, the closure of the set of generic elliptic periodic orbits contains hyperbolic sets with Hausdorff dimension arbitrarily close to maximal. Other instances of the restricted n-body problem such as the Sitnikov problem and the case n = 4 are also considered.

2025-06-23T00:00:00Z