Low dimensional multimodal maps

• Grant number: 14/09418-0
• Support type: Scholarships in Brazil - Post-Doctorate
• Effective date (Start): November 01, 2014
• Effective date (End): October 17, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Edson de Faria
• Grantee: Sofía Trejo Abad
• Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 11/16265-8 - Low dimensional dynamics, AP.TEM

Abstract

The project is focussed on the study of one dimensional multimodal maps. In particular, I will work towards the generalisation to the multimodal case of the renormalization results obtained by Avila and Lyubich for unimodal maps, where they showed the exponential contraction of the renormalization operator along hybrid classes. I will make use of the results I obtain on renormalization to prove that infinitely renormalizable multimodal maps have measure zero within generic families; a key result needed to settle the Palis conjecture in the multimodal case. Finally, I will study critical circle maps with more than one critical point with the aim of proving rigidity.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

CLARK, TREVOR; TREJO, SOFIA. The boundary of chaos for interval mappings. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, v. 121, n. 6, p. 1427-1467, DEC 2020. Web of Science Citations: 0.

CLARK, TREVOR; VAN STRIEN, SEBASTIAN; TREJO, SOFIA. Complex Bounds for Real Maps. Communications in Mathematical Physics, v. 355, n. 3, p. 1001-1119, NOV 2017. Web of Science Citations: 1.