Continua of central configurations with a negative mass in the n-body problem |
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Authors: | Julian Hachmeister John Little Jasmine McGhee Roberto Pelayo Spencer Sasarita |
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Institution: | 1. University of Hawai’i at Hilo, Hilo, HI, USA 2. Department of Mathematics and Computer Science, College of the Holy Cross, Worcester, MA, USA 3. Loyola Marymount University, Los Angeles, CA, USA 4. Department of Mathematics, University of Hawai’i at Hilo, Hilo, HI, USA 5. University of Arizona, Tucson, AZ, USA
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Abstract: | The number of equivalence classes of central configurations of $n \le 4$ bodies of positive mass is known to be finite, but it remains to be shown if this is true for $n \ge 5$ . By allowing one mass to be negative, Gareth Roberts constructed a continuum of inequivalent planar central configurations of $n = 5$ bodies. We reinterpret Roberts’ example and generalize the construction of his continuum to produce a family of continua of central configurations, each with a single negative mass. These new continua exist in even dimensional spaces $\mathbb R ^k$ for $k \ge 4$ . |
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