The dynamics of Kepler equation

• Autores: Víctor Lanchares Barrasa , Iván Luis Pérez Barrón
• Localización: Monografías de la Real Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza, ISSN 1132-6360, Nº. 22, 2003, págs. 75-82
• Idioma: inglés
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• Resumen

  • It is well known that Kepler¿s equation can be solved by means of an iterative method defined, in a natural way, from the equation itself. This method yields to the unique solution if the eccentricity is in the range of the elliptic orbits. However, if we allow the eccentricity to take values greater than one or even in the complex plane, we discover a rich dynamics where period doubling bifurcations cascades are found, as well as fractal structures.