Sustainable Development Goals
Research interests
• Dynamics in the restricted n-body problems
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Central configurations
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Periodic orbits in the n-body problems with weak and strong potentials
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Integrability and periodic orbits of Hamiltonian systems
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Stability
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Nonlinear dynamical systems
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Ordinary differential equations
Profile
Professor Martha Álvarez Ramírez studied Mathematics at the Universidad Autónoma de San Luis Potosí (UASLP), obtaining her degree in 1988 with the thesis, A mathematical model of bruselosis, directed by Dr. Ignacio Barradas from CIMAT (Guanajuato). She studied for a master's degree in Mathematics at the Universidad Autónoma Metropolitana (UAM) Iztapapala Campus with the thesis, periodic orbits in the pendulum-spring, under the direction of Dr. Joaquín Delgado. Ph.D. in Applied Mathematics at the Autonomous University of Barcelona (Spain), where she obtained her degree in 1997, with a thesis focused on the 3-body problem with primaries in an elliptical collision orbit, directed by Dr. Jaume Llibre. In 1997 she joined the Mathematics Department of the UAM Iztapalapa Campus as a Professor. She is also a member of the National System of Researchers since 1998, currently at level II.
Her research is focused on the qualitative theory of ordinary differential equations, celestial mechanics, and Hamiltonian systems. In collaboration with colleagues from Mexico and other countries, he has written about 40 research articles, which have been published in international indexed journals. Her research is focused on central configuration for flat 4- and 5-body problems, integrability in Hamiltonian systems, ejection-collision orbits, averaging methods to study periodic orbits, oscillatory motions in restricted N-body problems and the use of differential geometry techniques in the N-body problem as a geodesic flow in Riemannian varieties.
She has supervised one doctoral, four master's, and six bachelor's theses. She is currently supervising three Ph.D. and one M.S.
She has refereed articles in the following research journals: Physics Letters A, Astrophysics and Space Science, Monthly Notices of the Royal Astronomical Society, Journal of King Saud University (Science), International Journal of Astronomy and Astrophysics (IJAA), Celestial Mechanics and Dynamical Astronomy, The Journal of the Astronautical Sciences, Advances in Space Research, Qualitative Theory of Dynamical Systems, Nonlinear Analysis: Real World Applications, International Journal of Non Linear Mechanics, Journal of Mathematical Analysis and Applications.
She is a reviewer of published mathematical articles for the databases Mathematical Reviews (MathSciNet) of the American Mathematical Society (AMS) and Zentralblatt für Mathematik (zbMATH) of the European Mathematical Society (EMS).
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