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Dr. Uribe-Santibañez, Marco
Research Outputs
Zero‐Hopf bifurcation in the generalized Hiemenz equation
2021, Dr. Uribe-Santibañez, Marco, Martínez, Elisa
In this work, we show the existence of zero-Hopf periodic orbits in a 10-parametric differential equation of third order x′′′ + (a1x′ + b1x + c1)x′′ + (a2x′ + b2x + c2)x′ + (a3x′ + b3x + c3)x + k = 0, where ai, bi, ci, k ∈ R for i = 1, 2, 3. This family is based on a generalization of the equation associated to the Hiemenz flow, when the boundary conditions are neglected, and it will be named as generalized Hiemenz equation. Our approach relies in the use of averaging method. Moreover, the kind of stability of the periodic orbits is determined according to the parameters.
Number of zeros of complete abelian integrals for a primitive rational polynomial with non-trivial global monodromy
2020, Dr. Uribe-Santibañez, Marco, Rebollo-Perdomo, Salomón
We provide explicit lower and upper bounds for the maximum number of isolated zeros of the complete Abelian integral associated with a rational polynomial, with non-trivial global monodromy, and a polynomial 1-form of degree n. Moreover, we obtain the explicit form of the relative cohomology of the polynomial 1-forms with respect to the rational polynomial.
Existence and stability of periodic orbits for a Hamiltonian system with homogeneous potential of degree five
2023, Dr. Uribe-Santibañez, Marco, Quispe, Margarita
In this paper we consider the autonomous Hamiltonian system with two degrees of freedom associated to the function H = ½ (x2 + y2) + ½ (p2/x + p2/y) + V5(x, y), where V5(x, y) = (A/5x5 + Bx3y2 + C/5 xy4) which is related to a homogeneous potential of degree five. We prove the existence of different families of periodic orbits and the type of stability is analyzed through the averaging theory which guarantee the existence of such orbits on adequate sets defined by the parameters A, B, C.