PreprintarXiv licencearXiv
Fifth-Harmonic Feedback Controls the Existence of a Third-Harmonic Zero
Abstract
An exact zero of a generated harmonic needs two real cancellations; a damped oscillator's leading fundamental-source balance supplies one. Absorber loss leaves a phase deficit of fixed sign, amplitude independent at leading order, closed instead by the orbit's own 5Ω motion returning to 3Ω at weight |Δ1|4. Closure is therefore unreachable at weak amplitude: the channel supplying it ranks at O(F7), not at the leading O(F3). The fifth harmonic is 1.8×10−3 of the relative-coordinate fundamental, yet a balance homotopy weighting it below $0.48$ annihilates the tracked pair in a saddle-node.
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BibTeX
@misc{sarkar2026fifthharmonic,
title = {{Fifth-Harmonic Feedback Controls the Existence of a Third-Harmonic Zero}},
author = {Kanchan Sarkar},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01508},
eprint = {2609.01508},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01508},
}
RIS
TY - UNPB
TI - Fifth-Harmonic Feedback Controls the Existence of a Third-Harmonic Zero
AU - Kanchan Sarkar
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01508
UR - https://arxiv.org/abs/2609.01508
AB - An exact zero of a generated harmonic needs two real cancellations; a damped oscillator's leading fundamental-source balance supplies one. Absorber loss leaves a phase deficit of fixed sign, amplitude independent at leading order, closed instead by the orbit's own 5Ω motion returning to 3Ω at weight |Δ_1|^4. Closure is therefore unreachable at weak amplitude: the channel supplying it ranks at O(F^7), not at the leading O(F^3). The fifth harmonic is 1.8×10^−3 of the relative-coordinate fundamental, yet a balance homotopy weighting it below $0.48$ annihilates the tracked pair in a saddle-node.
ER -