We show that given a general a priori unstable Hamiltonian $$\begin{aligned} \frac{1}{2} p^2 + V(q) + G(I) + \epsilon h(p, q, I, \varphi , t), \end{aligned}$$ 1 2 p 2 + V ( q ) + G ( I ) + ϵ h ( p , q , I , φ , t ) , where h is a generic Mañé analytic function and $$\epsilon $$ ϵ is small enough, there is an orbit for which the momentum I changes by any arbitrarily prescribed value. We call this phenomenon as global diffusion since the size of the change in I is independent of both $$\epsilon $$ ϵ and h. The fact that the pendulum and rotor variables are uncoupled is used essentially in our proof. The proof is based on simple and constructive geometrical methods, carefully studying the reduced Poincaré functions of the problem which generate the corresponding scattering maps.

# JISD 2025 ##### 21st School on Interactions between Dynamical Systems and Partial Differential Equations # JISD 2025 Sign in Advanced course / School From June 30, 2025 to July 04, 2025 The registration fee is 200€ / 75€ for lodging granted (includes coffee breaks and lunch) Registration deadline 12 / 06 / 2025 LECTURERS SCHEDULE POSTER SESSION & GRANTS Posters Introduction The School on Interactions between Dynamical Systems and Partial Differential Equations (JISD) is an international summer school that has taken place at the School of Mathematics and Statistics of the Universitat Politècnica de Catalunya (UPC) since 2002. The last five editions have been held at the Centre de Recerca Matemàtica (CRM). The JISD is an annual meeting between experts and young researchers in Dynamical Systems and Partial Differential Equations (PDEs). It is designed to encourage and enhance the exchange of knowledge and methods, with the goal of advancing the study of cutting-edge problems in the aforesaid fields of mathematics and with the aim of fostering interaction among the participants. The symposium is aimed at local researchers, as well as scientists from the rest of Spain and foreign countries. It is organized into four advanced courses of about 7 hours and complemented by a poster session by young researchers. Throughout the latest editions, the attendance numbers have ranged between 60 and 100 participants, mostly internationals. A primary objective of the JISD is to attract talented young researchers who can present a poster to put them in a position to benefit from exposure to world-leading experts and help them establish working relationships that could prove critical for their short- and long-term success. An especially strong effort has been devoted in past years to encourage the participation of undergraduates, PhDs and postdocs from developing countries and, more generally, young researchers who may encounter difficulties in accessing adequate financial support. JISD PAST EDITIONS lecturers ### **_AVERAGING AND FERMI ACCELERATION_** #### Dmitry Dolgopyat ##### University of Maryland **Abstract:** Averaging is one of classical tools in dynamics. However, despite two centuries of work, there are still many open problems. In this course I will illustrate some recent results and open problem in a model case of Fermi acceleration where one would like to describe the evolution of energy for a particle with the environment. WEBSITE ### _**NONLOCAL MINIMAL SURFACES**_ #### Serena Dipierro ##### University of Western Australia **Abstract** : We present the theory of nonlocal minimal surfaces, with special attention to interior regularity, sheeting phenomena, maximum principle, boundary stickiness and connection with phase transitions. WEBSITE ### **_RIGIDITY RESULTS AND BOCHNER TYPE TECHNIQUES IN RIEMANN GEOMETRY_** #### Luciano Mari ##### Università degli Studi di Milano Statale **Abstract** : This minicourse aims to introduce some techniques used to prove splitting and topological/geometric rigidity theorems in Riemannian Geometry. I will highlight how the stability/finite index of a Schrodinger operator naturally appearing in the problem forces the rigidity phenomenon. Among the applications, time permitting I will discuss some results in Schoen-Yau’s theory of harmonic maps, Li-Tam-Wang’s theory of Harmonic functions, and minimal (hyper)surfaces. WEBSITE ### **_DYNAMICAL DECOMPOSITIONS OF SURFACE DIFFEOMORPHISMS_** #### Sylvain Crovisier ##### Université Paris-Saclay Abstract: In order to describe the dynamics of a diffeomorphism, one first try to decompose the system into invariant elementary pieces, that may be studied separately. For hyperbolic dynamics, the decomposition is provided by Smale’s « spectral decomposition theorem », and the number of pieces is finite. These lectures deal with the decomposition of general smooth diffeomorphisms on surfaces. One will mainly focus on systems which have infinitely many pieces: typical examples have been constructed by Newhouse. Several view points will be covered: topological (filtration, renormalization) or measurable (Borel homoclinic classes). In good cases, the dynamics inside each piece may be studied as for uniformly hyperbolic systems: most of their orbits equidistribute towards natural invariant measures (physical or maximizing the entropy), and their statistics are described by limit theorems. I will also discuss how the dynamics degenerates along sequences of distinct pieces, in terms of their dynamical invariants (e.g. the entropy and the Lya-punov exponents). WEBSITE schedule | MONDAYJune 30th| TUESDAYJuly 1st| WEDNESDAYJuly 2nd| THURSDAYJuly 3rd| FRIDAYJuly 4th ---|---|---|---|---|--- **9:30****10:00**| **WELCOME**| ** _AVERAGING AND FERMI ACCELERATION_** -**Dmitry Dolgopyat** University of Maryland| ** _NONLOCAL MINIMAL SURFACES_** -**Serena Dipierro** University of Western Australia| ** _RIGIDITY RESULTS AND BOCHNER TYPE TECHNIQUES IN RIEMANN GEOMETRY_** -**Luciano Mari** Università degli Studi di Milano Statale| ** _DYNAMICAL DECOMPOSITIONS OF SURFACE DIFFEOMORPHISMS_** -**Sylvain Crovisier** Université Paris-Saclay **10:00****11:00** | ** _NONLOCAL MINIMAL SURFACES_** -**Serena Dipierro** University of Western Australia **11:00****11:30**| **COFFEE BREAK**| **GROUP PICTURE +****COFFEE BREAK**| **COFFEE BREAK** **11:30****13:00**| ** _AVERAGING AND FERMI ACCELERATION_** -**Dmitry Dolgopyat** University of Maryland| ** _RIGIDITY RESULTS AND BOCHNER TYPE TECHNIQUES IN RIEMANN GEOMETRY_** -**Luciano Mari** Università degli Studi di Milano Statale| ** _RIGIDITY RESULTS AND BOCHNER TYPE TECHNIQUES IN RIEMANN GEOMETRY_** -**Luciano Mari** Università degli Studi di Milano Statale| ** _DYNAMICAL DECOMPOSITIONS OF SURFACE DIFFEOMORPHISMS_** -**Sylvain Crovisier** Université Paris-Saclay| ** _NONLOCAL MINIMAL SURFACES_** --**Serena Dipierro** University of Western Australia **13:00****15:00**| **LUNCH**| -**_AVERAGING AND FERMI ACCELERATION_** -**Dmitry Dolgopyat** University of Maryland **LUNCH** **15:00****16:00**| ** _DYNAMICAL DECOMPOSITIONS OF SURFACE DIFFEOMORPHISMS_** -**Sylvain Crovisier** Université Paris-Saclay| ** _DYNAMICAL DECOMPOSITIONS OF SURFACE DIFFEOMORPHISMS_** -**Sylvain Crovisier** Université Paris-Saclay| ** _AVERAGING AND FERMI ACCELERATION_** -**Dmitry Dolgopyat** University of Maryland| ** _NONLOCAL MINIMAL SURFACES_** -**Serena Dipierro** University of Western Australia| **16:15****17:15**| ** _RIGIDITY RESULTS AND BOCHNER TYPE TECHNIQUES IN RIEMANN GEOMETRY_** -**Luciano Mari** Università degli Studi di Milano Statale| ** _NONLOCAL MINIMAL SURFACES_** -**Serena Dipierro** University of Western Australia| ** _DYNAMICAL DECOMPOSITIONS OF SURFACE DIFFEOMORPHISMS_** -**Sylvain Crovisier** Université Paris-Saclay| ** _AVERAGING AND FERMI ACCELERATION_** -**Dmitry Dolgopyat** University of Maryland **17:15****18:45**| **RECEPTION****+****POSTER SESSION**| **COFFEE BREAK**| | ** _RIGIDITY RESULTS AND BOCHNER TYPE TECHNIQUES IN RIEMANN GEOMETRY_** -**Luciano Mari** Università degli Studi di Milano Statale POSTER SESSION INFORMATION Participants have the option to contribute with a poster presentation. Posters have to measure 841mm x 1189mm (A0). To apply, please select the relevant option during the registration process. **_IMPORTANT_** : if applying for a poster presentation in the registration process, it will also be necessary to fill in the following **_JISD 2025 –questionnaire for grant and poster presentation applicants._** Resolutions and the information on how to proceed for payment will be sent by the deadline indicated below: * Deadline: **April 21, 2025**. * Resolutions will be sent by **May 19, 2025**. grants – CLOSED In order to increase the number of young researchers participating in this activity, the CRM offers grants to partially cover the registration fee and lodging on-campus (**grant reduced fee: 75€ for those receiving a lodging grant**). To apply, you must complete the registration process. Please go to **SIGN IN** , on the top of the web, choose the “** _general registration”_** and in the ** _OTHERS_ _section_** the ** _grant_ **you wish to apply for, you will be asked to attach your **CV**. Please click on the _**Reservation** _option before finishing the process. **__** **_IMPORTANT_** : if applying for a grant and/or a presentation in the registration process, it will also be necessary to fill in the following **_JISD 2025 – questionnaire for grant and poster presentation applicants._** Resolutions and the information on how to proceed for payment will be sent by the deadline indicated below: The application deadline for grants is **April 21, 2025**. --- Resolutions will be sent by **May 19, 2025.** Organising Committee **Xavier Cabré​** | ICREA – ​Universitat Politècnica de Catalunya – CRM ---|--- **Amadeu Delshams​** | ​Universitat Politècnica de Catalunya – CRM **Mar Giralt** | IMCCE at Observatoire de Paris **​Marcel Guàrdia​** | ​​Universitat de Barcelona – CRM **Tomás Sanz** | Universitat de Barcelona – CRM **Tere M. Seara​** | ​Universitat Politècnica de Catalunya – CRM scientific committee **Scott Armstrong** | Courant Institute, New York University ---|--- **Jean Pierre Eckmann ​** | ​Université de Genève **​Jean-Michel Roquejoffre** | ​Paul Sabatier University **​Susanna Terracini** | ​Università de Torino LIST OF PARTICIPANTS Name | Institution ---|--- Illya Koval | Institute of Science and Technology Austria Victor Medeiros | IMPA Juhee Sohn | Korea National University of Transportation Margherita Marcotullio | Gran Sasso Science Institute Angia Lauri | Gran Sasso Science Institute Mar Giralt Miron | Observatoire de Paris Sylvain Crovisier | University Paris-Saclay - CNRS Sylvain Crovisier | CNRS Tomás Sanz Perela | Universitat de Barcelona Francesc Timoner Vaquer | Universitat de Barcelona Joan Domingo Pasarin | Universitat de Barcelona Sara Guaitoli | Universitat de Barcelona Alejandro Martínez Sánchez | Universitat de Barcelona Gyula Csato | Universitat de Barcelona Marcel Guardia Munárriz | Universitat de Barcelona Xavier Cabré Vilagut | Universitat Politècnica de Catalunya Renzo Bruera | Universitat Politècnica de Catalunya Albert Mas Blesa | Universitat Politècnica de Catalunya Andrew Clarke | Universitat Politècnica de Catalunya Joan Solà-Morales | Universitat Politècnica de Catalunya José Lamas Rodríguez | Universitat Politècnica de Catalunya Rosa Maria Delicado Moll | Universitat Politècnica de Catalunya Joana Pech Alberich | Universitat Politècnica de Catalunya Olli Saari | Universitat Politècnica de Catalunya Gerard Codina | Universitat Politècnica de Catalunya Fernando Muñoz | Universitat Politècnica de Catalunya Víctor Villegas-Morral | Universitat Politècnica de Catalunya Santiago Barbieri | Universitat Politècnica de Catalunya Matteo Pandolfi | Universitat Politècnica de Catalunya Maria Teresa Martinez-Seara Alonso | Universitat Politècnica de Catalunya Amadeu Delshams i Valdés | Universitat Politècnica de Catalunya Otto Osterman | University of Maryland Dimtry Dolgopyat | University of Maryland Jaime Paradela | University of Maryland Serena Dipierro | University of Western Australia Edhin Mamani | Federal University of Minas Gerais Huub de Jong | University of British Columbia Sallah eddine Boutiah | Laval University Yuanlin Sun | Jilin University Brandon Hinostroza | Pierre-and-Marie-Curie University Mingmin Zhang | Paul Sabatier University - Toulouse III Kira Engelhardt | Leipzig University Luciano Mari | University of Milan Davide Giovagnoli | University of Bologna Stefano Baranzini | University of Turin Lorenzo Baroni | Roma Tre University Gerard Castro López | Swiss Federal Institute of Technology in Zurich Miriam Lorenzo | University of Cambridge Marc Homs-Dones | University of Warwick Joaquim Duran i Lamiel | Centre de Recerca Matemàtica Dídac Gil Rams | Centre de Recerca Matemàtica Alberto Maione | Centre de Recerca Matemàtica Søren István | Centre de Recerca Matemàtica Registration The registration fee (200€/75€ for granted) includes coffee breaks and lunch. * You will be asked to create a **_CRM web user account_** before registering to the activity through the following link: CRM USER CREATION **INVOICE/PAYMENT INFORMATION** **_IF YOUR INSTITUTION COVERS YOUR REGISTRATION FEE_** : Please note that, in case your institution is paying for the registration via bank transfer, you will have to indicate your institution details and choose “**Transfer** ” as the payment method at the end of the process. ##### UPF | UB | UPC | UAB *If the paying institution is the **UPF / UB/ UPC / UAB** , after registering, please send an email to comptabilitat@crm.cat with your name and the institution **internal reference number** that we will need to issue the electronic invoice. Please, send us the Project code covering the registration if needed. ##### Paying by credit card **_IF YOU PAY VIA CREDIT CARD_** but you need to provide the invoice to your institution to be reimbursed, please note that we will also need you to send an email to comptabilitat@crm.cat providing the**internal reference number given by your institution** and the code of the Project covering the registration (if necessary). **LODGING INFORMATION** ON-CAMPUS AND BELLATERRA BARCELONA AND OFF-CAMPUS ACKNOWLEDGEMENTS | For inquiries about this event please contact the Scientific Events Coordinator Ms. Núria Hernández at nhernandez@crm.cat​​ ---|--- scam warning We are aware of a number of current scams targeting participants at CRM activities concerning registration or accommodation bookings. If you are approached by a third party (eg travellerpoint.org, Conference Committee, Global Travel Experts or Royal Visit) asking for booking or payment details, please ignore them. Please remember: i) CRM never uses third parties to do our administration for events: messages will come directly from CRM staff ii) CRM will never ask participants for credit card or bank details iii) If you have any doubt about an email you receive please get in touch Stefano Baranzini | University of Turin​ | Periodic points for singular systems ---|--- Lorenzo Baroni | Roma Tre University​ | Linear Flow on the Innite Torus Huub de Jong | University of British Columbia​ | On Least Period Sets of Finitely Presented Systems Sallah Eddine Boutiah | Laval University​ | Keller-Segel type nite particle system with critical attracting interactions, and on the corresponding SDEs Davide Giovagnoli | University of Bologna​ | Free boundary regularity for the inhomogeneous Stefan Problem Marc Homs | University of Warwick​ | Minimal bifurcation diagram of torus flows Edhin Mamani | Federal University of Minas Gerais​ | On Lagrangian foliations invariant by the geodesic flow of manifolds without conjugate points Juhee Sohn | Korea National University of Transportation​ | Stability of solutions for the Maxwell-Chern-Simons model