Martin Andersson's homepage
Hi! I’m a mathematician working in the field of dynamical systems. My research focuses on topics in smooth ergodic theory (Lyapunov exponents, SRB measures, stable ergodicity) and robust transitivity. I have some experience with partial hyperbolicity, but am currently interested in general questions about the dynamics of non-invertible maps (endomorphisms). I am particularily interested in the interplay between large scale properties of a system (action of a diffeomorphism in homology groups) and infinitesimal analysis, such as Lyapunov exponents.
But how did I become interested in dynamical systems? Well, as an undergrad, I flirted with applied mathematics and mathematical physics. But I was also curious about “Chaos Theory”, which I had encountered in pop science literature. Halfway through my studies I had the pleasure of taking a course in ODEs, taught by Stefano Luzzatto. There I was introduced to some fascinating mathematical ideas, including Smale’s Horseshoe and rudimentary ergodic theory. It was a point of no return. I was hooked!
I hold an MSci degree in mathematics from Imperial College (2002) obtained under the supervision of Stefano Luzzatto and a Ph.D. from Instituto Nacional de Matemática Pura e Aplicada (2007) under the supervision of Marcelo Viana. I have also held postdoc positions at PUC-Rio, ICMC-USP, and ENS-PSL, as well as long term visits to Peking University (2014), IMJ-PRG (2018) and Laboratoire des Matématiques d’Orsay (2019).
Published papers:
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Partially hyperbolic endomorphisms with expanding linear part
(with Wagner Ranter). Ergodic Theory and Dynamical Systems, 45:321-336, 2025. -
Historic behaviour vs. physical measures for irrational flows with multiple stopping points (with Pierre-Antoine Guihéneuf). Advances in Mathematics, 409:108626, 2022.
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Statistical stability of mostly expanding diffeomorphisms (with Carlos H. Vásquez). Annales de l’Institut Henri Poincaré – Analyse Non Linéaire, 37:1245–1270, 2020.
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Transitivity of conservative diffeomorphisms isotopic to Anosov on T³ (with Shaobo Gan). Ergodic Theory and Dynamical Systems, 38:1–9, 2018.
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On mostly expanding diffeomorphisms (with Carlos H. Vásquez). Ergodic Theory and Dynamical Systems, 38:2838–2859, 2018.
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Transitivity of conservative toral endomorphisms. Nonlinearity, 29:1047–1055, 2016.
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Ergodic Theory of Generic Continuous Maps (with Flavio Abdenur). Communications in Mathematical Physics, 318:831–855, 2013.
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Robust ergodic properties in partially hyperbolic dynamics. Transactions of the American Mathematical Society, 362:1831–1867, 2010.
Accepted for publication:
- Non-uniformly hyperbolic endomorphisms (with Pablo Carrasco and Radu Saghin). To appear in Compositio Mathematica.
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Most of my teaching load goes to teaching calculus for engineering and science students. Apart from that I have also taught the following courses:
- Analysis on the real line
- Functional Analysis
- Measure and Integration
- Ordinary Differential Equations
- Introduction to Dynamical Systems
- Dynamical Systems I
- Ergodic Theory I
Current Ph.D. students:
- Jefferson Victor de Sousa Galvão
- Zusana Cecilia Verástegui Muñoz
Current Masters students:
- Luiz Gabriel Ferreira Penna Lopes da Silva
Past Masters students:
- Caio Caetano Aguiar
Martin Andersson
Professor Associado
Departamento de Matemática Aplicada
Universidade Federal Fluminense
Sala 15, Bloco G, Campus do Gragoatá
