PreprintCC BY 4.0arXiv
Lyapunov-Schmidt reduction for periodic orbits of implicit discrete dynamical systems
Abstract
We derive bifurcation equations for periodic orbits of autonomous and periodically non-autonomous implicit discrete systems in arbitrary finite dimension. Cyclic Lyapunov--Schmidt reduction gives recursive coefficients and nondegeneracy and transversality conditions at the multipliers +1 and -1. We prove equivalence under regular changes of implicit representation and exact invariance under cyclic relabelling when the reduction data are transported consistently.
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BibTeX
@misc{oliveira2026lyapunovschmidt,
title = {{Lyapunov-Schmidt reduction for periodic orbits of implicit discrete dynamical systems}},
author = {Henrique M. Oliveira},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03336},
eprint = {2611.03336},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03336},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Lyapunov-Schmidt reduction for periodic orbits of implicit discrete dynamical systems
AU - Henrique M. Oliveira
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03336
UR - https://arxiv.org/abs/2611.03336
AB - We derive bifurcation equations for periodic orbits of autonomous and periodically non-autonomous implicit discrete systems in arbitrary finite dimension. Cyclic Lyapunov--Schmidt reduction gives recursive coefficients and nondegeneracy and transversality conditions at the multipliers +1 and -1. We prove equivalence under regular changes of implicit representation and exact invariance under cyclic relabelling when the reduction data are transported consistently.
ER -