Publicación: CONTINUATION AND BIFURCATIONS OF CONCAVE CENTRAL CONFIGURATIONS IN THE FOUR AND FIVE BODY-PROBLEMS FOR HOMOGENEOUS FORCE LAWS
Fecha
2017
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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Resumen
THE CENTRAL CONFIGURATIONS GIVEN BY AN EQUILATERAL TRIANGLE AND A REGULAR TETRAHEDRON WITH EQUAL MASSES AT THE VERTICES AND A BODY AT THE BARYCENTER HAVE BEEN WIDELY STUDIED IN [9] AND [14] DUE TO THE PHENOMENA OF BIFURCATION OCCURRING WHEN THE CENTRAL MASS HAS A DETERMINED VALUE
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. WE PROPOSE A VARIATION OF THIS PROBLEM SETTING THE CENTRAL MASS AS THE CRITICAL VALUE
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AND LETTING A MASS AT A VERTEX TO BE THE PARAMETER OF BIFURCATION. IN BOTH CASES, 2D AND 3D, WE VERIFY THE EXISTENCE OF BIFURCATION, THAT IS, FOR A SAME SET OF MASSES WE DETERMINE TWO NEW CENTRAL CONFIGURATIONS. THE COMPUTATION OF THE BIFURCATIONS, AS WELL AS THEIR PICTURES HAVE BEEN PERFORMED CONSIDERING HOMOGENEOUS FORCE LAWS WITH EXPONENT .
