Seminar Day - UB-UPC DSG
📅 When: 16:00, December 17th
📍 Where: Aula T2 (2n pis), Facultat de Matemàtiques i Informàtica, UB.
🧑 Who:: Domènec Ruiz i Balet (UB)
📔Title: Connections between dynamical systems, deep learning and large language models
Abstract: This introductory talk aims to introduce some of the most relevant machine learning architectures and understand them as dynamical systems. We will navegate through formulations, different problems and perspective and some of the current results.
Seminar Day - UB-UPC DSG
📅 When: 16:00, December 10th
📍 Where: Aula T2 (2n pis), Facultat de Matemàtiques i Informàtica, UB.
🧑 Who: Illya Koval (IST Austria)
📔Title: Fractal-like meanders appear in KAM theory
Abstract:
In KAM theory, a certain nondegeneracy of the Hessian of the unperturbed Hamiltonian is crucial to show the existence of invariant tori.
These invariant tori have to be the graphs of Lipschitz functions. However, when such a type of nondegeneracy is violated, very little is known. Inspired by the works of Simó, we will show the existence of non-graph meandering invariant tori and that they are generic. We discuss meanders of the first order, second order, and even fractal-like meanders. This is a joint work in progress with Vadim Kaloshin and Yi Pan.
Seminar Day - UB-UPC DSG
📅 When: 16:00, December 3
📍 Where: Aula T2 (2n pis), Facultat de Matemàtiques i Informàtica, UB.
🧑 Who: Frank Trujillo (CRM)
📔Title: Hausdorff Dimension of Invariant Measures of AIETs
Abstract:
In this talk, we will discuss the Hausdorff dimension of invariant measures of affine interval exchange transformations (AIETs). AIETs are piecewise affine bijections of a bounded interval with a finite number of discontinuities. In general, these maps are uniquely ergodic, and their unique invariant probability measure is singular with respect to Lebesgue measure.
We will provide explicit values for the Hausdorff dimension of this unique invariant probability measure for a particular class of AIETs, called self-similar AIETs.
This is joint work with P. Berk, K. Frączek, and Ł. Kotlewski.
On equilateral central configurations in the \(1+4\) -body problem now in Communications in Nonlinear Science and Numerical Simulation from our colleagues E. Barrabés and J.M. Cors and their collaborators M. Álvarez-Ramírez.
Check it out here to learn more:https://www.sciencedirect.com/science/article/pii/S1007570425007749
Seminar Day - UB-UPC DSG
📅 When: 16:00, November 26th
📍 Where: Aula S04, FME-UPC.
🧑 Who: Anna Gierzkiewicz (Jagiellonian University)
📔Title: Detecting oscillating orbits in the Sitnikov 3BP by computer assistance
Abstract:
In a joint work with M. Capiński and P. Martín, we prove the existence of oscillatory orbits (i.e., orbits that go closer and closer to infinity but always return to a fixed bounded region) for the Sitnikov 3BP in the case of three equal masses (\(m_1 = m\)).
The proof relies on analyzing the stable and unstable invariant manifolds of infinity and their intersections.
We construct orbits shadowing these invariant manifolds by the method of correctly aligned windows.
The proof is computer assisted with the use of CAPD library for C++.
Kahan-Hirota-Kimura maps preserving original cubic Hamiltonians now in Mathematics and computers in simulation from our colleagues V. Mañosa and C. Pantazi.
Check it out here to learn more:https://www.sciencedirect.com/science/article/pii/S0378475425001855
Capturing the short-term characteristics of a barred galaxy from a single snapshot now in Communications in nonlinear science and numerical simulation from our colleagues P. Sánchez and J. Masdemont and their collaborator J. Amorós.
Check it out here to learn more: https://www.sciencedirect.com/science/article/pii/S100757042500334X
Seminar Day - UB-UPC DSG - Double Session
📅 When: 17:15, November 12th.
📍 Where: Aula S03, FME-UPC.
🧑 Who: Sergi Burniol Clotet (Universidad de la República, Uruguai)
📔Title: Rigidity of the Unstable Foliation
Abstract: Anosov flows are one of the central examples of hyperbolic and chaotic dynamical systems. Associated to them are the stable and unstable foliations, whose leaves contract and expand exponentially along the flow. In this talk, we present a rigidity result for these foliations in the case of transitive Anosov flows on 3-manifolds: if the unstable foliations of two such flows are equivalent (that is, if there exists a homeomorphism mapping one foliation to the other), then the flows are topologically conjugate up to a constant change of time.
The classical examples of Anosov flows are the geodesic flows of compact negatively curved surfaces. In this setting, there are previous rigidity results due to Ratner, Marcus, and Abe, among others. The latter showed that if the unstable foliations of two such flows are equivalent, then the underlying surfaces are homothetic.
Seminar Day - UB-UPC DSG - Double Session
📅 When: 16:00, November 12th.
📍 Where: Aula S03, FME-UPC.
🧑 Who: Guowei Yu (Nankai University)
📔Title: (Bi)-hyperbolic and (bi)-parabolic motions in the restricted (N+1)-body problem
Abstract: According to Chazy, the final motion of the restricted (N+1)-body problem has four possibilities: bounded, hyperbolic, parabolic and oscillatory. When the motion is hyperbolic or parabolic, the massless body will go to infinity along a definite asymptotic direction with a finite limiting energy. Then there are two basic questions: First given any initial time and position, as well as the asymptotic direction and limiting energy when time goes to positive infinity, is there a corresponding hyperbolic or parabolic motion realizing it; Second given any asymptotic directions and limiting energy, when time goes to both negative and positive infinity, it there a corresponding bi-hyperbolic or bi-parabolic motion realizing it? In this talk, we will report some of our progress in these two questions.
Capturing the short-term characteristics of a barred galaxy from a single snapshot now in Communications in nonlinear science and numerical simulation from our colleagues P. Sánchez and J. Masdemont and their collaborators .
Check it out here to learn more:https://www.sciencedirect.com/science/article/pii/S100757042500334X
Temporary capture about the Moon involving Sun?Earth libration point dynamics now in Communications in nonlinear science and numerical simulation from our colleagues J.J. Masdemont and his collaborators B. Pang and D. Qiao.
Check it out here to learn more:https://www.sciencedirect.com/science/article/abs/pii/S1007570425002035
Great 8th Barcelona Dynamic Systems Day! Key highlights:
🧠 "Clar que sí. Hi ha sistemes dinàmics dins la nostra ment" by Catalina Vich.
🪐 "Sobre l'estabilitat d'un sistema planetari Sol-Júpiter-Saturn" by Alex Haro.
🏆 Barcelona Dynamical Systems Prize: "Benjamin-Feir instability of Stokes waves" by Massimiliano Berti, Alberto Maspero & Paolo Ventura.
A brilliant day of maths and community. Congrats to the winners and thanks to all!
#DynamicalSystems #Maths #Neuroscience #SolarSystem #Barcelona #8JSD
Weakly asymptotically quasiperiodic solutions for time-dependent Hamiltonians with a view to celestial mechanics now in Journal of differential equations from our colleagues D. Scarcella.
Check it out here to learn more:https://www.sciencedirect.com/science/article/abs/pii/S0022039625001883
Generic global diffusion for analytic a priori unstable systems now in Communications in mathematical physics from our colleagues A. Delshams and his collaborators K. Zhang.
Check it out here to learn more:https://link.springer.com/article/10.1007/s00220-025-05342-1
Seminar Day - UB-UPC DSG
📅 When: 16:00, October 15th
📍 Where: Aula S04, FME, UPC
🧑 Who: : Otto Vaughn Osterman
University of Maryland
📔Title: Length Spectrum Rigidity in Dispersing Billiard Systems
Abstract: The problem of spectral rigidity in dispersing billiard systems is that of determining whether the perimeters of periodic orbits uniquely determine the billiard table up to isometry. We consider this problem for the class of dispersing billiard systems consisting of three convex scatterers in the plane satisfying the non-eclipse condition. We show that the perimeters of a particular set of periodic orbits for two such systems are identical if and only if their collision maps are locally analytically conjugated to each other near a particular homoclinic orbit.
On March we missed some more papers:
Firing rate distributions in plastic networks of spiking neurons now in Network neuroscience from our colleague M. Vegué and her collaborators A. Allard and P. Desrosiers.
Check it out here to learn more:https://direct.mit.edu/netn/article/9/1/447/127594/Firing-rate-distributions-in-plastic-networks-of
Global bifurcation in a virus, defective genomes, satellite RNAs tripartite system: breakdown of a coexistence quasi-neutral curve now in Chaos, solitons & fractals from our colleague T. Lazaro and his collaborators O. Llopis, S. Elena and J. Sardanyès.
Check it out here to learn more:https://www.sciencedirect.com/science/article/abs/pii/S0960077925000505
We are glad to share that our colleague Jezabel Curbelo has won the price "Premi Nacional d'Investigació".
https://mat.upc.edu/ca/noticies/jezabel-curbelo-premi-nacional-dinvestigacio-2025
Seminar Day - UB-UPC DSG
📍 Where: Aula S04, Facultat de Matemàtiques i Estadística, UPC. Pau Gargallo,14 BCN.
📅 When: 16:00, September 1st
🧑 Who: Robert Cardona, Universitat de Barcelona
📔Title: Beyond helicity: dynamical invariants of 3D volume-preserving flows and a conjecture of Arnold and Khesin
Abstract: Volume-preserving flows on 3-manifolds arise naturally in fluid dynamics and plasma physics, where the vorticity or magnetic field is transported by the motion of the fluid. A central role is played by the helicity, a classical invariant introduced by Woltjer and Moffatt that measures the average linking of flow lines. Helicity is the best-known “coadjoint invariant” of a volume-preserving flow, which implies that it is preserved under the natural symmetries of the fluid equations, and it enjoys important uniqueness properties among such invariants.
In this talk, which is meant to be accessible, I will first explain and motivate the relevant notions, and then focus on the question of how
far the uniqueness of helicity really goes. In particular, I will show that the Ruelle invariant is, in a precise sense, everywhere independent of helicity in the C^1-topology. This gives a strong negative answer to the C^1-case of a conjecture of Arnold and Khesin.
This is joint work with Julian Chaidez (University of Southern California) and Francisco Torres de Lizaur (Universidad de Sevilla).
A new update of some publications that we missed in January.
Admitted when breastfeeding: impact and experiences of hospital care now in Breastfeeding medicine from our colleague
@joaquimpuig and his collaborators A. Llupia, A. Lladó and L. Aguilar.
Check it out here to learn more: https://pubmed.ncbi.nlm.nih.gov/39831804/
Breakdown of homoclinic orbits to L3: nonvanishing of the stokes constant now in Discrete and continuous dynamical systems. Series A from our colleagues I. Baldomà and her collaborators M. Capinski, M. Giralt and M. Guardia.
Check it out here to learn more: https://www.aimsciences.org/article/doi/10.3934/dcds.2024086
On a Countable Sequence of Homoclinic Orbits Arising Near a Saddle–Center Point, now in Communications in Mathematical Physics from our colleague I. Baldomá and his collaborators M. Guardia and D. E. Pelinovsky.
Check it out here to learn more:
https://link.springer.com/article/10.1007/s00220-025-05381-8