Scientific Interests

Dynamical systems and ergodic theory: generic properties of dynamical systems, symplectic dynamics, random dynamical systems, billiard dynamics, Lyapunov exponents and linear cocycles, topological dynamics, spectral theory of graphs

Research project:  Member of the research project  New Trends in Lyapunov Exponents  FCT PTDC/MAT-PUR/29126/2017 (past)

In preparation

• Assis Azevedo, Davide Azevedo, Mário Bessa and Maria Joana Torres, Most volume-preserving Sobolev maps have zero Lyapunov exponents and are transitive,  in preparation

• Alexandre Baraviera, Pedro Duarte and Maria Joana Torres, Growth inequalities, in preparation

• Alexandre Baraviera, Pedro Duarte, Longmei Shu and Maria Joana Torres, General renewal shift, in preparation

• Mário Bessa, Maria Joana Torres and Paulo Varandas, Cº-generic (Lipschitz) vector fields generate ergodic flows, in preparation

• Mário Bessa, João Lopes Dias and Maria Joana Torres, Generic Symplectic homeomorphisms are strongly transitive, in preparation

• Mário Bessa, João Lopes Dias, Gianluigi Del Magno, José Pedro Gaivão e Maria Joana Torres, Genericity and stability of expansiveness among convex bodies, in preparation

• Mário Bessa, Jaqueline Siqueira, Maria Joana Torres and Paulo Varandas, Generic properties of continuous impulsive semiflows,  in preparation

Preprints

• Assis Azevedo, Davide Azevedo, Mário Bessa and Maria Joana Torres, Genericity of ergodicity for Sobolev homeomorphisms, arXiv:2504.18993 (2025)

Publications

• J. Siqueira, M.J. Torres and P. Varandas, Abundance of periodic orbits for typical impulsive semiflows,  Journal of Differential Equations, 448 (2025), 113703. 

• Mário Bessa, João Lopes Dias, Pedro Matias and Maria Joana Torres, Positive Topological Entropy for Semi-Riemannian Geodesic Flows,  Proceedings of the American Mathematical Society, 153 (9) (2025), 3987–3998.

• Alexandre Baraviera, Pedro Duarte, Longmei Shu and Maria Joana Torres, Isospectral reductions of non-negative matrices, Applied Mathematics and Computation, 499 (2025), 129402.

• Mário Bessa, Gianluigi Del Magno, João Lopes Dias, José Pedro Gaivão and Maria Joana Torres, Billiards in generic convex bodies have positive topological entropy, Advances in Mathematics, 442 (2024), 109592.

• Alexandre Baraviera, Pedro Duarte and Maria Joana Torres, Synchronization of coupled map lattices, Proceedings of the Edinburgh Mathematical Society, 66(1) (2023), 143-163.

• Alexandre Baraviera, Pedro Duarte and Maria Joana Torres,  Stationary measures on infinite graphs, Communications in Contemporary Mathematics,  24(7) (2022), 2150025.

• Mário Bessa, João Lopes Dias and Maria Joana Torres, Expansiveness and Hyperbolicity in Convex Billiards, Regular and Chaotic Dynamics, 26(6) (2021), 756-762

• Mário Bessa, Maria Joana Torres and Paulo Varandas, Topological aspects of incompressible flows, Journal of Differential Equations, 293 (2021), 392-417.

• Thiago Bomfim, Maria Joana Torres and Paulo Varandas, The gluing orbit property and partial hyperbolicity, Journal of Differential Equations, 272 (2021), 203-221

• Assis Azevedo, Davide Azevedo, Mário  Bessa and Maria Joana Torres, The closing lemma and the planar general density theorem for Sobolev maps,  Proceedings of the American Mathematical Society, 149(4) (2021), 1687–1696

• Pedro Duarte and Maria Joana Torres, Isospectral Reduction in Infinite Graphs, Journal of Spectral Theory,  10(3) (2020), 955-989

• Mário Bessa, João Lopes Dias and Maria Joana Torres, Hyperbolicity through stable shadowing for generic geodesic flows, Physica D: Nonlinear Phenomena, 406 (2020), 132423

•  Mário Bessa and Maria Joana Torres, There are no proper topological hyperbolic homoclinic classes for area-preserving maps, Proceedings of the Edinburgh Mathematical Society, 63(1) (2020), 217--228

• Assis Azevedo, Davide Azevedo, Mário  Bessa and Maria Joana Torres, Sobolev homeomorphisms are dense in volume preserving automorphisms, Journal of Functional Analysis, 276(10) (2019), 3261--3274

• Mário Bessa, Maria Joana Torres and Paulo Varandas, On the periodic orbits, shadowing and strong transitivity of continuous flows, Nonlinear Analysis, 175 (2018), 191--209

• Thiago Bomfim, Maria Joana Torres and Paulo Varandas. Topological features of flows with the reparametrized gluing orbit property, Journal of Differential Equations, 262 (2017), 4292--4313

• Mário Bessa, João Lopes Dias and Maria Joana Torres, On shadowing and hyperbolicity for geodesic flows on surfaces, Nonlinear Analysis: Theory, Methods and Applications, 155 (2017), 250--263

• Pedro Duarte and Maria Joana Torres, r-Regularity, Journal of Mathematical Imaging and Vision, 51(3) (2015), 451--464

• Pedro Duarte and Maria Joana Torres, Eigenvectors of isospectral graph transformations, Linear Algebra and its Applications, 474(1) (2015), 110--123

• Mário Bessa and Maria Joana Torres, The C0-general density theorem for geodesic flows, Comptes Rendus Mathematique. Académie des Sciences Paris, 353 (6) (2015), 545--549

• Pedro Duarte and Maria Joana Torres, Smoothness of boundaries of regular sets, Journal of Mathematical Imaging and Vision, 48(1) (2014), 106--113

• Mário Bessa, Jorge Rocha and Maria Joana Torres, Hyperbolicity and stability for Hamiltonian flows, Journal of Differential Equations, 254(1) (2013), 309--322

• Mário Bessa, Jorge Rocha  and Maria Joana Torres, Shades of hyperbolicity for Hamiltonians, Nonlinearity, 26 (2013), 2851--2873

• Pedro Duarte and Maria Joana Torres, A discrete Faà di Bruno's formula,  Contributions to Discrete Mathematics, 7(2) (2012), 72--83

• Pedro Duarte and Maria Joana Torres, Spectral stability of Markov systems, Nonlinearity 21(3) (2008), 381--397

• Pedro Duarte and Maria Joana Torres, Combinatorial stability of non-deterministic systems, Ergodic Theory and Dynamical Systems 26 (2006), 93--128

Conference proceedings

•  Mário Bessa, Jorge Rocha  and Maria Joana Torres, Estabilidade de Hamiltonianos, Boletim da Sociedade Portuguesa de Matemática, Special issue (2016), 125--128

• Pedro Duarte and Maria Joana Torres, Stability of non-deterministic systems, From Particle Systems to Partial Differential Equations II, Springer Proceedings in Mathematics Statistics, Volume 129 (2015), ed. A. J. Soares, P. Gonçalves, 193--207

CIM Bulletin

•  Maria Joana Torres, Generic behaviours of conservative systems, CIM Bulletin, 44 (2022), 19-26

Other publications

• Maria Joana Torres, Winning Nim with Beatty and Fibonacci, Proceedings of the Recreational Mathematics Colloquium II, University of Évora, Portugal, April 27-30 (2011), Associação Ludus, 113--125

• Ricardo Severino and Maria Joana Torres, Order and chaos: interactive computational activities for the classroom, Proceedings of ICTMT10: The Tenth International Conference on Technology in Mathematics Teaching, University of Portsmouth, Portsmouth, United Kingdom,  July 5-8 (2011), 267--272 

Wolfram Notebook Archive

• Alexandre Baraviera, Pedro Duarte and Maria Joana Torres, Stationary measures on infinite graphs, Wolfram Notebook Archive (2022)

Some talks

• Isospectral reduction and its applications to network dynamics, Fourth ANAP meeting, UTAD, Vila Real, 3 Outubro (2025)

• A panorama of isospectral reduction and its applications to graph dynamics, Workshop on Optimization, Dynamics and Convex Analysis, Universidade de Aveiro, 11-14 Junho (2025)

• Generic behaviours of dynamical systems, Manhãs de Matemática na AbERTA - Sistemas Dinâmicos, 6 de Julho (2023)

• Generic behaviours of dynamical systems, 2nd Women Meeting in Mathematics, University of Minho, 7-9 Setembro (2022)

• Sistemas dinâmicos em grafos, XVII Escola de Verão em Matemática na Universidade Federal do Espírito Santo, Brasil, 3 Fevereiro (2022)

• Stationary measures on infinite graphs , Quinto Workshop de Sistemas Dinâmicos - Universidade Federal do Rio Grande do Sul, Brasil, 6-7 Dezembro (2021)

• The closing lemma and the planar general density theorem for Sobolev maps, Encontro Nacional da SPM 2021, online, 12-16 Julho (2021)

• On the gluing orbit property - topological features and its relation with partial hyperbolicity, Seminário no Instituto de Matemática - Universidade Federal do Rio de Janeiro, Brasil, 2 Dezembro (2020)

• Stability and shades of hyperbolicity for Hamiltonians and geodesic flows, Symposium in Dynamical Systems on the occasion of Jorge Rocha 60th birthday, 14 Outubro (2020)

• Redução iso-espectral em grafos infinitos, Encontro Nacional da SPM 2018, Instituto Politécnico de Bragança, Portugal,  9-11 Julho (2018)

• Actualização dos vectores próprios em redução iso-espectral de grafos, Encontro Nacional da SPM 2016, Escola Superior de Tecnologia do Barreiro do Instituto Politécnico de Setúbal, Portugal, 11-13 Julho (2016)

• Estabilidade de Hamiltonianos, Encontro Nacional da SPM 2014, Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa, Campus da Caparica, Portugal, 14-16 Julho (2014)

• Stability of non-deterministic systems, Particle Systems and Partial Differential Equations II, Braga, Portugal, 12-13 December 2013

• On C2-stability of Hamiltonians, Planet Earth, Dynamics, Games and Science II, Fundação Calouste Gulbenkian, Lisboa, Portugal, 2-4 September 2013

• Stability and shades of hyperbolicity for Hamiltonians, 3rd One Day Meeting on Dynamical Systems, Centre for Applied Mathematics and Economics, ISEG-Technical University of Lisbon, Portugal, 12 December (2012)

• Stability and Morse decompositions of non-deterministic systems, 6th Workshop on Statistics, Mathematics and Computation and 3rd Portuguese-Polish Workshop on Biometry in Honour of Professor Dinis Pestana, Covilhã, Portugal, 3-4 July 2012

• Order and chaos: interactive computational activities for the classroom, ICTMT10: The Tenth International Conference on Technology in Mathematics Teaching, University of Portsmouth, Portsmouth, United Kingdom, 5-8 July 2011

• Winning Nim with Beatty and Fibonacci, Recreational Mathematics Colloquium II, Universidade de Évora, Portugal, 27-30 April 2011

• Estabilidade Combinatória de Sistemas Dinâmicos Não-Determinísticos, Universidade de Évora, Portugal, May 13 (2011)