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School and Conference on Dynamical Systems

ICTP Mathematics via YouTube

Overview

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Conference covering advanced topics in dynamical systems theory through a comprehensive two-week program featuring expert lectures and research presentations. Explore five major areas of dynamical systems including chaotic dynamics with homoclinic bifurcations, attractors, and partial hyperbolicity; conservative dynamics encompassing KAM theory, Hamiltonian systems, and celestial mechanics; ergodic theory focusing on Sinai-Ruelle-Bowen measures and Lyapunov exponents; geometric and topological aspects of dynamics; and one-dimensional dynamics examining hyperbolicity and parametrized families. Attend three core lecture series delivered by leading researchers: Applications of homogeneous dynamics from number theory to statistical mechanics by Jens Marklof and Andreas Strömbergsson, Renormalization in low dimensional dynamics by Marco Martens, and Partially hyperbolic diffeomorphisms by Sylvain Crovisier and Rafael Potrie. Access over 50 specialized research talks covering cutting-edge developments in thermodynamics for non-uniformly hyperbolic maps, Lorenz attractors, ergodic averages, equilibrium states, billiards, geodesic flows, and rigidity theory. Gain exposure to both theoretical foundations and current research frontiers in dynamical systems through presentations by internationally recognized experts in the field.

Syllabus

Applications of homogeneous dynamics - Jens Marklof & Andreas Strombergsson - Lecture 01
Applications of homogeneous dynamics - Jens Marklof & Andreas Strombergsson - Lecture 02
Applications of homogeneous dynamics - Jens Marklof & Andreas Strombergsson - Lecture 03
Applications of homogeneous dynamics - Jens Marklof & Andreas Strombergsson - Lecture 04
Applications of homogeneous dynamics - Jens Marklof & Andreas Strombergsson - Lecture 05
Applications of homogeneous dynamics - Jens Marklof & Andreas Strombergsson - Lecture 06
Applications of homogeneous dynamics - Jens Marklof & Andreas Strömbergsson - Lecture 07
Applications of homogeneous dynamics - Jens Marklof & Andreas Strombergsson - Lecture 08
Applications of homogeneous dynamics - Jens Marklof & Andreas Strombergsson - Lecture 09
Applications of homogeneous dynamics - Jens Marklof & Andreas Strombergsson - Lecture 10
Partially hyperbolic diffeomorphisms - Sylvain Crovisier & Rafael Potrie - Lecture 01
Partially hyperbolic diffeomorphisms - Sylvain Crovisier & Rafael Potrie - Lecture 02
Partially hyperbolic diffeomorphisms - Sylvain Crovisier & Rafael Potrie - Lecture 03
Partially hyperbolic diffeomorphisms - Sylvain Crovisier & Rafael Potrie - Lecture 04
Partially hyperbolic diffeomorphisms - Sylvain Crovisier & Rafael Potrie - Lecture 05
Partially hyperbolic diffeomorphisms - Sylvain Crovisier & Rafael Potrie - Lecture 06
Partially hyperbolic diffeomorphisms - Sylvain Crovisier & Rafael Potrie - Lecture 07
Partially hyperbolic diffeomorphisms - Sylvain Crovisier & Rafael Potrie - Lecture 08
Partially hyperbolic diffeomorphisms - Sylvain Crovisier & Rafael Potrie - Lecture 09
Partially hyperbolic diffeomorphisms - Sylvain Crovisier & Rafael Potrie - Lecture 10
Renormalization in low dimensional dynamics - Marco Martens - Lecture 01
Renormalization in low dimensional dynamics - Marco Martens - Lecture 02
Renormalization in low dimensional dynamics - Marco Martens - Lecture 03
Renormalization in low dimensional dynamics - Marco Martens - Lecture 04
Renormalization in low dimensional dynamics - Marco Martens - Lecture 05
Renormalization in low dimensional dynamics - Marco Martens - Lecture 06
Renormalization in low dimensional dynamics - Marco Martens - Lecture 07
Renormalization in low dimensional dynamics - Marco Martens - Lecture 08
Renormalization in low-dimensional dynamics - Marco Martens - Lecture 09
Renormalisation in low-dimensional dynamics - Marco Martens - Lecture 10
Building Thermodynamics for Non-uniformly Hyperbolic maps - Yakov Pesin
On the robustness of intermingled basins - Rual Ures
Convergence of non conventional ergodic averages - Idris Assani
Contracting Lorenz Attractor: statistical properties - Maria Jose Pacifico
Center-unstable foliatoins do not have compact leaves - Jana Rodriguez-Hertz
Almost sure continuity along curves traversing the Mandelbrot set - Michael Benedicks
Continuity of entropy map for nonuniformly hyperbolic systems - Wenxiang Sun
Recurrence on inifinite cyclic covering - Albert Fathi
Perihelia reduction for the planetary problem with applications - Gabriella Pinzari
Equilibrium states for some partially hypberbolic maps - Krerley Oliveira
On the finiteness of attractors for piecewise $C^2$ maps of the interval - Vilton Pinheiro
On error term of the prime periodic orbit theorem for expanding semiflows - Masato Tsujii
The ergodic properties of the Kusuoka measure - Mark Pollicott
Measure and smooth rigidity of lattice actions in low dimensions - Federico Rodriguez-Hertz
Invariant pseudo-foliations for minimal homeomorphisms in dimension 2 - Alejandro Kocsard
On the fractal geometry of horseshoes in arbitrary dimensions - Carlos Moreira
Rempe model and Denjoy odometer - Mitsuhiro Shishikura
Expansive models - Rafael Oswaldo Ruggiero Rodriguez
Stochastic dynamics from a deterministic one - Domokos Szasz
Fictitious games - Sebastian van Strien
Holder regularity of solutions of the cohomological equations for IET's - Stefano Marmi
Geometric pressure in real and complex 1D dynamics - Feliks Przytycki
Some properties of entropy for C^r interval maps - David Burguet
On stability of elliptic fixed points and tori - Bassam R. Fayad
Diffusion of wind-tree billiards and Lyapunov exponents of the Hodge - Anton Zorich
Unique equilibrium states for geodesic flows in nonpositive curvature - Keith Burns
Three fundamental problems concerning codimension-one foliations - Andres Navas
Fatou flowers and parabolic curves - Marco Abate
Geodesic flows on surfaces with non positive curvature that are Bernoulli - Yuri Lima
On rigidity theory for circle maps with breaks - Konstantin Khanin
Determinantal point processes and their quasi-symmetries - Alexander Bufetov
Almost reducibility for the linear quasi-periodic wave-equation - Hakan Eliasson
Eaton lenses, pseudo-integrable billiards and genericity along curves - Corinna Ulcigrai
The multiplicity of measures of maximum entropy - Jerome Buzzi
Sensitive dependence of geometric Gibbs measures - Juan Rivera-Letelier
Sharp mixing rates via inducing w.r.t. general return times - Henk Bruin
Singular vector fields far away from horseshoe - Shaobo Gan

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