Publications

Research: My main interests are Topological Dynamics on surfaces and Bifurcation Theory of vector fields, including global dynamics and classification of injective maps. I am also interested on dynamical systems with symmetry and applications to Differential Equations. Recently, I am curious about Numerical Analysis and applications to Engineering.

Publications:

– B. Alarcón, S.B.S.D. Castro and I. S. Labouriau. Global Saddles for Planar Maps. Journal of Dynamics and Differential Equations, 30, 601–612, 2018. DOI 10.1007/s10884-016-9561-3.

– B. Alarcón and R. Rabanal. Hopf bifurcation at infinity and dissipative vector fields of the plane. Proceedings of the American Mathematical Society, 145, 3033-3046, 2017. DOI 10.1090/proc/13462.

– B. Alarcón, S.B.S.D. Castro and I. S. Labouriau. Discrete Symmetric Planar Dynamics. Dynamics, Games and Science CIM Series in Mathematical Sciences, Springer. Vol. I, Chap. 2, 2015.

– B. Alarcón. Rotation numbers for planar attractors of equivariant homeomorphisms. Topological Methods in Nonlinear Analysis, 42 n.2, 327-343, 2013.

– B. Alarcón, S.B.S.D. Castro and I. S. Labouriau. Global Dynamics for Symmetric Planar Maps. Discrete & Continuous Dyn Syst- A, 37, 2241-2251, 2013.

– B. Alarcón, S.B.S.D. Castro and I. S. Labouriau. A local but not global attractor for a Zn-symmetric map. Journal of Singularities, 6, 1-14, 2012.

– B. Alarcón, S.B.S.D. Castro and I. S. Labouriau. The Discrete Markus-Yamabe Problem for Symmetric Planar Polynomial Maps. Indagationes Mathematicae, 23, 603–608, 2012.

– B. Alarcón, V. Guiñez and C. Gutierrez. Planar Embeddings with a globally attracting fixed point. Nonlinear Analysis, 69, 140-150, 2008.

– B. Alarcón, C. Gutierrez and J. Martínez-Alfaro. Planar maps whose second iterate has a unique fixed point. Journal of Difference Equations and Applications, 14 n. 4, 421-428, 2008.

– B. Alarcón, V. Guiñez and C. Gutierrez. Hopf bifurcation at infinity for planar vector fields. Discrete and Continuous Dynamical Systems A, 17 n. 2, 247-258, 2007.