Banca de DEFESA: TALITA SANTOS DE ARAUJO

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : TALITA SANTOS DE ARAUJO
DATE: 16/02/2024
TIME: 10:00
LOCAL: online
TITLE:

Stable Intersections of Cantor sets

KEY WORDS:

Regular Cantor Sets, Stable Intersection of Cantor Sets, Arithmetic Difference of Cantor Sets.

PAGES: 120
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUBÁREA: Geometria e Topologia
SPECIALTY: Sistemas Dinâmicos
SUMMARY:

In this work, we study stable intersections and arithmetic differences of regular Cantor sets.

We present techniques that help us to detect the existence of stable intersections or extremals stable intersections between pairs of Cantor sets. We start with the Gap Lemma of Newhouse, which uses the thickness of the Cantor sets to this conclusion, the Generalized Thickness Test, which studies the intersection of Markov domains and finally, the existence of a recurrent compact in space of the relative configurations of these Cantor sets.

We also present some examples that show how such techniques are applied registered. In certain examples, we highlight that one of the techniques works, while the others may fail, thus showing the importance of studying each one from them.

We finish with a brief study of the topology of the arithmetic difference of affine Cantor sets, presenting a family of Cantor sets whose the arithmetic difference is almost always an R-Cantorval.

COMMITTEE MEMBERS:
Presidente - 2362244 - DAVI DOS SANTOS LIMA
Interno(a) - 1226894 - RAFAEL NOBREGA DE OLIVEIRA LUCENA
Externo(a) à Instituição - SERGIO AUGUSTO ROMAÑA IBARRA - UFRJ
Externo(a) à Instituição - CARLOS GUSTAVO TAMM DE ARAÚJO MOREIRA - IMPA