Lectures related to Invariant measure

A Conjecture of Erdös: Proof by Moreira, Richter and Robertson

Presents a short proof of a conjecture by Erdös, exploring related questions and detailed proof of the proposition.

FK-Percolation and the Six-Vertex Model: Critical Phenomena

Covers the transition from the six-vertex model to FK-percolation, focusing on critical phenomena and phase transitions in two-dimensional systems.

Structure of Measure-Preserving Systems

Covers the abstract structure of measure-preserving systems and aims to understand their classification and ergodic decompositions.

Ergodic Theory: Chaos

Explores elements from Ergodic Theory, transformations, invariant sets, and Lyapunov Exponents for 1-dimensional maps.

Introduction to Quantum Chaos

Covers the introduction to Quantum Chaos, classical chaos, sensitivity to initial conditions, ergodicity, and Lyapunov exponents.

Invariant Measures: Properties and Applications

Covers the concept of invariant measures in Markov chains and their role in analyzing irreducible recurrent processes.

Applications of Ergodic Theory to Combinatorics

Explores the applications of ergodic theory to combinatorics and number theory, including Szemerédi's Theorem and the Erdős-Kac Theorem.

Mixing Properties of Infinite Measure Preserving Systems

Explores mixing properties of infinite measure preserving systems, focusing on suspensions, Govers transformations, and Lorentz gas.

Theory & Practice of Kalman Filter

Covers the theory and practice of Kalman Filter in Matlab.

Equidistribution of CM Points

Explores the equidistribution of CM points and the implications of ergodicity in measure-preserving systems.

Gibbs measures: Hyperbolic Attractors

Explores Gibbs measures for hyperbolic attractors, including T-invariant probability measures and perturbations of the CAT map.

Infinitesimal Deformations: One-Dimensional Maps

Explores infinitesimal deformations of one-dimensional maps, discussing common characteristics, methods, and recent results in expanding and piecewise expanding maps.

Newton's Method for Dynamical Systems

Explores Newton's method for dynamical systems, GMRES, FGMRES, optimization, multishooting, and trust-region methods.

Z-Transforms: Poles and Zeros

Explores Z-Transforms, Poles, Zeros, and their applications in discrete-time systems and Linear Time-Invariant systems.

Dynamical Systems: Laplace Transform

Covers the Laplace transform, transfer functions, and properties of common functions in dynamical systems.

LTI Systems Properties

Covers the properties of Linear Time-Invariant (LTI) systems and their implications.

Linear Time Invariant Systems: Impulse Response and Convolution

Covers linear time invariant systems, focusing on impulse response and convolution.

Signal and System Analysis: Impulse Response and Convolution

Covers the analysis of LTI systems using impulse response and convolution.

Markov Chains: General Concepts

Covers the general concepts of Markov chains and their applications in various fields.

Discrete-time Systems and Lyapunov Theory

Covers the review of linear discrete-time systems and Lyapunov theory, focusing on stability and equilibria.