Publications

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Published papers:

[1] M. Bessa, Dynamics of generic 2-dimensional linear differential systems, Journal of Differential Equations, vol. 228 – 2, 685-706, 2006.

[2] M. Bessa, J. Rocha, Removing zero Lyapunov exponents in volume-preserving flows, Nonlinearity, Vol 20, nº 4, 1007-1016, 2007.

[3] M. Bessa, The Lyapunov exponents of zero divergence three-dimensional vector fields, Ergodic Theory and Dynamical Systems, Vol 27, nº 5, 1445-1472, 2007.

[4] M. Bessa, Dynamic of generic multidimensional linear differential systems, Advanced Nonlinear Studies, Vol 8, 191-211 , 2008.

[5] M. Bessa, J. Rocha, On the fundamental regions of a fixed point free conservative Hénon map, Bulletin of the Australian Mathematical Society, Vol 77, nº 1, 37-48, 2008.

[6] M. Bessa, J. L. Dias, Generic dynamics of 4-dimensional C2 Hamiltonian systems, Communications in Mathematical Physics, Vol 281, nº 1, 597-619, 2008.

[7] V. Araújo, M. Bessa, Dominated splitting and zero volume for incompressible three-flows, Nonlinearity, Vol 21, nº 7, 1637-1653, 2008.

[8] M. Bessa, P. Duarte, Abundance of elliptic dynamics on conservative 3-flows, Dynamical Systems – An international Journal, Vol 23, nº 4, 409-424, 2008.

[9] M. Bessa, J. Rocha, On C1-robust transitivity of volume-preserving flows , Journal of Differential Equations, vol. 245 – 11, 3127-3143, 2008.

[10] M. Bessa, M. Carvalho, On the spectrum of infinite dimensional random products of compact operators , Stochastics & Dynamics, vol. 8 – 4, 593-611, 2008.

[11] M. Bessa, Generic incompressible flows are topological mixing, Comptes Rendus Mathematique vol. 346, 1169-1174, 2008.

[12] M. Bessa, J. L. Dias, Hamiltonian elliptic dynamics on symplectic 4-manifolds, Proceedings of the American Mathematical Society, vol. 137,   585-592, 2009.

[13] M.Bessa, Are there chaotic maps in the sphere? Chaos, Solitons & Fractals, vol. 42, nº1, 235-237, 2009.

[14] M. Bessa, J. Rocha, Homoclinic tangencies versus uniform hyperbolicity for conservative 3-flows, Journal of Differential Equations, vol. 247,   2913-2923, 2009.

[15] M. Bessa, J. Rocha, Three-dimensional   conservative star flows are Anosov, Discrete and Continuous Dynamical Systems – A , vol 26, 3, 839-846, 2010.

[16] M. Bessa, C. Ferreira, J. Rocha, On the stability of the set of hyperbolic closed orbits of a Hamiltonian, Mathematical Proceedings of the Cambridge Philosophical Society, vol 149, 2, 373-383, 2010.

[17] M. Bessa, P. Varandas, On the entropy of conservative flows. Qualitative Theory of Dynamical Systems, vol 10, 1, 11-22, 2011.

[18] M. Bessa, J. Rocha, Denseness of ergodicity for a class of volume-preserving flows. Portugaliae Mathematica, vol 68, 1, 1-17, 2011.

[19] M. Bessa, J. Rocha, Topological stability for conservative systems, Journal of Differential Equations, vol 250, 10, 3960-3966, 2011.

[20] M. Bessa, J. Rocha, A remark on the topological stability of symplectomorphisms. Applied Mathematics Letters, vol 25, 2, 163-165, 2012.

[21] M. Bessa, C. Silva, Dense area-preserving homeomorphisms have zero Lyapunov exponents. Discrete and Continuous Dynamical Systems – A, vol 32, 4, 1231-1244, 2012.

[22] M. Bessa, Perturbations of Mathieu equations with parametric excitation of large period. Advances in Dynamical Systems and Applications, vol 7, 1, 17-30, 2012.

[23] M. Bessa, J. Rocha and M.J. Torres, Hyperbolicity and Stability for Hamiltonian flows. Journal of Differential Equations, vol 254, 1, 309-322, 2013.

[24] M. Bessa, M. Carvalho, Non-uniform hyperbolicity for infinite dimensional  cocycles. Stochastics & Dynamics vol 13, 3, 2013.

[25] M. Bessa, J. Rocha, M. J. Torres, Shades of Hyperbolicity for Hamiltonians. Nonlinearity, vol 26, 10, 2851-2873, 2013.

[26] M. Bessa, On C1-generic chaotic systems in three-manifolds. Qualitative Theory of Dynamical Systems, vol 12, 2, 323-334, 2013.

[27] M. Bessa, C1-stably shadowable conservative diffeomorphisms are Anosov. Bulletin of the Korean Mathematical Society, vol 50, 5, 1495-1499, 2013.

[28] M. Bessa, J. Rocha, Contributions to the geometric and ergodic theory of conservative flows. Ergodic Theory and Dynamical Systems, vol 33, 6, 1667-1708, 2013.

[29] M. Bessa, H. Vilarinho, Fine properties of Lp-cocycles which allows abundance of simple and trivial spectrum. Journal of Differential Equations, vol 256, 7, 2337-2367, 2014.

[30] M. Bessa, M. Lee, S. Vaz, Stable weakly shadowable volume-preserving systems are volume-hyperbolic. Acta Mathematica Sinica, vol 30, 6, 1007-1020, 2014.

[31] M. Bessa, S. Vaz, Stably weakly shadowing symplectic maps are partially hyperbolic. Communications of the Korean Mathematical Society, vol 29, 2, 285-293, 2014.

[32] M. Bessa, J. L. Dias, Hamiltonian suspension of perturbed Poincaré sections and an application, Mathematical Proceedings of the Cambridge Philosophical Society, vol 157, 1, 101-112, 2014.

[33] M. Bessa, M. Lee, X. Wen, Shadowing, expansiveness and specification for C1-conservative systems, Acta Mathematica Scientia, vol 35, 3, 583-600, 2015.

[34] M. Bessa, R. Ribeiro, Conservative flows with various types of shadowing, Chaos, Solitons & Fractals vol 75, 6, 243-252, 2015.

[35] M. Bessa, M. Carvalho, A. Rodrigues, Generic area-preserving reversing diffeomorphisms, Nonlinearity, vol 28, 6, 1695-1720, 2015.

[36] M. Bessa, M.J. Torres, The C0 general density theorem for geodesic flows, Comptes Rendus Mathematique, vol. 353, 6, 545-549 2015.

[37] M. Bessa, P. Varandas, Trivial and simple spectrum for SL(2,IR) cocycles with free base and fiber dynamics. Acta Mathematica Sinica, vol 31, 7, 1113-1122, 2015.

[38]M. Bessa and A. Rodrigues, Dynamics of conservative Bykov cycles: tangencies, generalized Cocoon bifurcations and elliptic solutions Journal of Differential Equations, Vol. 261, 2, 1176-1202, 2016.

[39] M. Bessa, S. Dias and A.A. Pinto, Explosion of differentiability for equivalences between Anosov flows on 3-manifolds. Proceedings of the American Mathematical Society, Vol. 144, 9, 3757-3766 2016.

[40] M. Bessa, A. Rodrigues, A Dichotomy in area-preserving reversible maps, Qualitative Theory of Dynamical Systems, Vol. 2, 309-326 2016.

[41] M. Bessa, M. Stadlbauer, On the Lyapunov spectrum of   relative transfer operators. Stochastics & Dynamics, Vol. 16, 6, 1650024, 25 pp.  2016.

[42] M. Bessa, C. Ferreira, J. Rocha and P. Varandas, Generic Hamiltonian dynamics. Journal of Dynamics and Differential Equations, Vol. 29, 203-218 2017.

[43] M. Bessa, J.L. Dias and M.J. Torres, On shadowing and hyperbolicity for geodesic flows on surfacesNonlinear Analysis: Theory, Methods & Applications, Vol. 155, 250-263 2017.

[44] M. Bessa, The flowbox theorem for divergence-free Lipschitz vector fields, Comptes Rendus Mathematique, Vol. 355, 8, 881–886, 2017.

[45] M. Bessa, J. Bochi, M. Cambrainha, C. Matheus, P. Varandas, D. Xu, Positivity of the top  Lyapunov exponent for cocycles on semisimple Lie groups over hyperbolic bases, Bulletin of the Brazilian Mathematical Society (2017) to appear.

 

Conference Proceeding & Book Chapters:

[1] V. Araújo, M. Bessa, M.J. Pacífico, Global Dynamics of Generic 3-flows (Chapter 9) in Three-dimensional flows, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 53 – Springer 2010 .

[2] M. Bessa, J. L. Dias, Generic Hamiltonian dynamical systems: an overview, 123-138, Dynamics, Games and Science- Vol. I, – Springer Proceedings in Mathematics 2011.

[3] M. Bessa, Area-preserving diffeomorphisms from the C1 standpoint, 181-212, Dynamics, Games and Science- Vol 2 – Springer Proceedings in Mathematics 2011.

 

 

Others:

[1] M. Bessa, Homeomorphisms of the plane without fixed points, Textos de Matemática CMUP, 2005-01. Portuguese (Master Thesis).

[2] M. Bessa, The Lyapunov exponents of conservative continuous-time dynamical systems, Teses de Doutorado IMPA, C048-2006. (PhD Thesis).

[3] M. Bessa, M. Carvalho, Frisos imperfeitos de números inteiros (Imperfect friezes of integers). Boletim da Sociedade Portuguesa de Matemática, vol 67, October, 201-208, 2012.

[4] M. Bessa, Tracing orbits on conservative maps, CIM Bulletin, 33 January, pp-27 2013.

[5] M. Bessa, J. Rocha, M. J. Torres, Estabilidade de Hamiltonianos. Boletim da Sociedade Portuguesa de Matemática,   Encontro Nacional da SPM (Sistemas Dinâmicos), Maio, 125–128, 2016.

[6]  M. Bessa, M. Carvalho, A. Rodrigues, A note on reversibility and Pell equationsBoletim da Sociedade Portuguesa de Matemática (2017).

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