# VN.RIO

## Validated Numerics for Dynamical Systems and Related Topics in Rio de Janeiro

School @UFRJ 18-22 February 2019

Workshop @IMPA 25 February-1 March 2019

## What is Validated Numerics?

Validated Numerics is a set of mathematical and numerical tools that allows us to prove mathematical results with the aid of a computer.

One of the most successful tecniques in the area is Interval Arithmetic, a computational framework that, in its most basic use, allows us to enclose the range of functions, i.e., given an interval I and a function f which takes values in the real numbers, we can find an interval that bounds the range of f over I automatically with the use of a computer.

While, in principle, this may seem quite limited, the applications of this simple process are striking: from bounding tails of series, root finding, enclosure of orbits of ODEs and dynamical systems, enclosures for values of integrals, and many others.

The goals of this summer program are to give an access point to researchers and students into the topic of Validated Numerics and to disseminate research results obtained with interval tecniques to the wider mathematical community.

## School in Validated Numerics @UFRJ (18- 22 February 2019)

The school in Validated Numerics at UFRJ aims to introduce students and researchers to the basic tools of Validated Numerics, with a view towards Computer-Assisted Proofs in Dynamical Systems.

We are going to follow the book:

**W. Tucker**

**Validated Numerics: A Short Introduction to Rigorous Computations, Princeton University Press **

The school will have morning lectures introducing the concepts of Validated Numerics, Computer Assisted Proofs and some basic notions of Dynamical Systems and afternoon exercise sessions in which we will replicate O.E. Lanford III enclosure of the value of the Feigenbaum constant (article).

We are currently checking if we can give some sort of financial support to participants.

(Image from Wikimedia https://commons.wikimedia.org/wiki/File:Logistic_map_bifurcation_diagram.png)

## Workshop in Validated Numerics @ IMPA (25 February - 1 March 2019)

This research workshop aims to disseminate recent results in Validated Numerics to a wider mathematical audience.

Some of the topics to be discussed are

- Ergodic and statistical properties of deterministic and random dynamics
- Renormalization
- Parameter exclusion

## Registration

To register to participate in the school or the workshop, fill this form.

The events are free and open to everyone but registration is necessary since space is limited and to allow access to the premises.

Organizing commitee:

- Isaia Nisoli (UFRJ)
- Luiz Henrique de Figueiredo (IMPA)
- Warwick Tucker (Uppsala University)