Work

A functional limit theorem for a dynamical system with an observable maximised on a Cantor set

Year: 2025

Type: article

Abstract: We consider heavy-tailed observables maximised on a dynamically defined Cantor set and prove convergence of the associated point processes as well as functional limit theorems. The Cantor structure, and its connection to the dynamics, causes clustering of large observations: this is captured in the ‘decorations’ on our point processes and functional limits, an application of the theory developed in a paper by the latter three authors.

Source: Physica D Nonlinear Phenomena

DOI: 10.1016/j.physd.2025.134989

Authors: Raquel Couto, Ana Cristina Moreira Freitas, Jorge Milhazes Freitas, Mike Todd

Institutions: Universidade do Porto, Centro de Matemática, University of St Andrews

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,640

Funders: Fundação para a Ciência e a Tecnologia, Centro de Matemática Universidade do Porto