Departamento de Matemática
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On certain homological invariant and its relation with poincaré duality pairs
(Algebra and Discrete Mathematics, 2018) [Artigo]Let G be a group, S = {Si, i ∈ I} a non empty family of (not necessarily distinct) subgroups of infinite index in G and M a ℤ2 Gmodule. In [4] the authors defined a homological invariant E∗ (G, S, M), which is “dual” to ... 
Nonchaotic Behavior in Quadratic ThreeDimensional Differential Systems with a Symmetric Jacobian Matrix
(International Journal of Bifurcation and Chaos, 2018) [Artigo]In this paper, we give an algebraic criterion to determine the nonchaotic behavior for polynomial differential systems defined in ℝ3 and, using this result, we give a partial positive answer for the conjecture about the ... 
Spectra of generalized stochastic adding machines
(Fundamenta Mathematicae, 2018) [Artigo]We define stochastic adding machines based on Cantor systems of numeration. We show that the spectra associated to these stochastic adding machines are fibered Julia sets, and we also compute various parts of the spectra ... 
Singular levels and topological invariants of Morse–Bott foliations on nonorientable surfaces
(Topological Methods in Nonlinear Analysis, 2018) [Artigo]We investigate the classification of closed curves and eight curves of saddle points defined on nonorientable closed surfaces, up to an ambient homeomorphism. The classification obtained here is applied to Morse–Bott ... 
Periodic orbits, invariant tori and chaotic behavior in certain nonequilibrium quadratic threedimensional differential systems
(Studies in Systems, Decision and Control, 2018) [Capítulo de livro]In (Jafari et al, Phys Lett A 377(9):699702, 2013) the authors gave the expressions of seventeen classes of quadratic differential systems defined in R3, depending on one real parameter a, which present chaotic behavior ... 
On the existence of periodic orbits and KAM tori in the Sprott A system: a special case of the Nosé–Hoover oscillator
(Nonlinear Dynamics, 2018) [Artigo]We consider the wellknown Sprott A system, which is a special case of the widely studied Nosé–Hoover oscillator. The system depends on a single real parameter a, and for suitable choices of the parameter value, it is shown ... 
Geometry of cuspidal edges with boundary
(Topology and its Applications, 2018) [Artigo]We study differential geometric properties of cuspidal edges with boundary. There are several differential geometric invariants which are related with the behavior of the boundary in addition to usual differential geometric ... 
The Reeb Graph of a Map Germ from R3 to R2 with Non Isolated Zeros
(Bulletin of the Brazilian Mathematical Society, 2018) [Artigo]We consider the topological classification of finitely determined map germs [f] : (R3, 0) → (R2, 0) with f 1(0) ≠ { 0 }. The case f 1(0) = { 0 } was treated in another recent paper by the authors. The main tool used to ... 
Regularization of discontinuous foliations: Blowing up and sliding conditions via Fenichel theory
(Journal of Differential Equations, 2017) [Artigo]We study the regularization of an oriented 1foliation F on M∖Σ where M is a smooth manifold and Σ⊂M is a closed subset, which can be interpreted as the discontinuity locus of F. In the spirit of Filippov's work, we define ... 
Stable ergodicity and accessibility for certain partially hyperbolic diffeomorphisms with bidimensional center leaves
(Commentarii Mathematici Helvetici, 2017) [Artigo]We consider classes of partially hyperbolic diffeomorphism f : M → M with splitting TM = Es ⊕ Ec ⊕ Eu and dim Ec = 2. These classes include for instance (perturbations of) the product of Anosov and conservative surface ... 
ZeroHopf bifurcation in a Chua system
(Nonlinear Analysis: Real World Applications, 2017) [Artigo]A zeroHopf equilibrium is an isolated equilibrium point whose eigenvalues are ±ωi≠0 and 0. In general for a such equilibrium there is no theory for knowing when it bifurcates some smallamplitude limit cycles moving the ... 
A hybrid symbolicnumerical approach to the centerfocus problem
(Journal of Symbolic Computation, 2017) [Artigo]We propose a new hybrid symbolicnumerical approach to the centerfocus problem. The method allowed us to obtain center conditions for a threedimensional system of differential equations, which was previously not possible ... 
C1Genericity of symplectic diffeomorphisms and lower bounds for topological entropy
(Dynamical Systems, 2017) [Artigo]There is a C1residual (Baire second class) subset R of symplectic diffeomorphisms on 2ddimensional manifold, d ≥ 1, such that for every nonAnosov f in R, its topological entropy is lower bounded by the supremum of the ... 
Exact boundary controllability for a series of membranes elastically connected
(Electronic Journal of Differential Equations, 2017) [Artigo]In this article we study the exact controllability with Neumann boundary controls for a system of linear wave equations coupled in parallel by lower order terms on piecewise smooth domains of the plane. We obtain square ... 
Topological Structural Stability of Partial Differential Equations on Projected Spaces
(Journal of Dynamics and Differential Equations, 2018) [Artigo]In this paper we study topological structural stability for a family of nonlinear semigroups Th(·) on Banach space Xh depending on the parameter h. Our results shows the robustness of the internal dynamics and characterization ... 
On the formation of hidden chaotic attractors and nested invariant tori in the Sprott A system
(Nonlinear Dynamics, 2017) [Artigo]We consider the wellknown Sprott A system, which depends on a single real parameter a and, for a= 1 , was shown to present a hidden chaotic attractor. We study the formation of hidden chaotic attractors as well as the ... 
The Reeb Graph of a Map Germ from ℝ3 to ℝ2 with Isolated Zeros
(Proceedings of the Edinburgh Mathematical Society, 2017) [Artigo]We consider finitely determined map germs f : (ℝ3, 0) → (ℝ2, 0) with f 1(0) = {0} and we look at the classification of this kind of germ with respect to topological equivalence. By Fukuda's cone structure theorem, the ... 
Dynamics of parabolic equations via the finite element method I. Continuity of the set of equilibria
(Journal of Differential Equations, 2016) [Artigo]In this paper we study the dynamics of parabolic semilinear differential equations with homogeneous Dirichlet boundary conditions via the discretization of finite element method. We provide an appropriate functional setting ... 
On the Heat Equation with Nonlinearity and Singular Anisotropic Potential on the Boundary
(Potential Analysis, 2017) [Artigo]This paper concerns with the heat equation in the halfspace ℝ+n with nonlinearity and singular potential on the boundary ∂ℝ+n. We show a wellposedness result that allows us to consider critical potentials with infinite ... 
Analyticity and near optimal time boundary controllability for the linear Klein–Gordon equation
(Journal of Mathematical Analysis and Applications, 2017) [Artigo]We study time analyticity for the solutions of the linear Klein–Gordon equation in RN, N≥1 and use it to obtain essentially optimal time boundary controllability in piecewise smooth domains. The initial state has finite ...