Julia sets, Vershik adic map and dynamic of operators

• Grant number: 15/26161-6
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: May 01, 2016
• End date: October 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Ali Messaoudi
• Grantee: Danilo Antonio Caprio
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
• Associated research grant: 13/24541-0 - Ergodic and qualitative theory of dynamical systems, AP.TEM
• Associated scholarship(s): 18/13720-5 - Bratteli diagrams, Rauzy fractals and Julia sets, BE.EP.PD

Abstract

The aim of this work is to study dynamical, topological and spectral properties for a class of operators associated to the stochastic adding machine. This study involves the following topics (among others): Stochastic adding machine, Vershik adic maps, Stochastic process and Markov chains, Dynamic of endomorphism of C^n, for n greater than 1, Julia sets in C^2 (and in R^2), Dynamic of linear operators in Banach spaces.

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)

BASTOS, JEFFERSON L. R.; CAPRIO, DANILO A.; MESSAOUDI, ALI. Shadowing and stability in p-adic dynamics. Journal of Mathematical Analysis and Applications, v. 500, n. 2, p. 28-pg., 2021-03-15. (19/10269-3, 13/24541-0, 15/26161-6)

CAPRIO, DANILO ANTONIO. Filled Julia set of some class of Henon-like maps. DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, v. 35, n. 1, SEP 2019. (18/13720-5, 15/26161-6)

CAPRIO, DANILO A.; MESSAOUDI, ALI; VALLE, GLAUCO. STOCHASTIC ADDING MACHINES BASED ON BRATTELI DIAGRAMS. ANNALES DE L INSTITUT FOURIER, v. 70, n. 6, p. 39-pg., 2020-01-01. (19/10269-3, 15/26161-6)