Orbital carriers and inheritance in discrete-time quadratic dynamics

Jason A. C. Gallas
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Jason A. C. Gallas: Instituto de Altos Estudos da Paraíba, Rua Silvino Lopes 419-2502, João Pessoa 58039-190, Brazil2Complexity Sciences Center, 9225 Collins Ave. Suite 1208, Surfside FL 33154, USA3Max-Planck-Institut für Physik komplexer Systeme, Dresden 01187, Germany

International Journal of Modern Physics C (IJMPC), 2020, vol. 31, issue 07, 1-16

Abstract: Explicit formulas for orbital carriers of periods 4, 5 and 6 are reported for discrete-time quadratic dynamics. A systematic investigation of orbital inheritance for periods as high as k≤12 is also reported. Inheritance means that unknown orbits may be obtained by nonlinear transformations of known orbits. Such nested orbit within orbit stratification shows orbits not to be necessarily independent of each other as generally assumed. Orbital stratification is potentially significant to rearrange trajectories sums in trace formulas underlying modern semiclassical interpretations of atomic physics spectra. The stratification seems to dominate as the orbital period grows.

Keywords: Orbital carriers; orbital inheritance; quadratic dynamics; symbolic computation (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0129183120501004

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