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PreprintCC BY 4.0arXiv

A New Route to Chaos through the Geometric Composition of Non-Normal Amplification

  • D. Sornette
  • V. R. Saiprasad
  • V. Troude
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Abstract

Chaos emerges when stretching is repeatedly recycled by reinjection. We uncover a new route to chaos in which the decisive variable is the temporal order of non-normal tangent maps: periodic and chaotic states can share essentially the same one-step stretching statistics while their ordered products acquire opposite Lyapunov growth. We introduce the ordered-product growth rate hL over L successive tangent maps, which reveals how states indistinguishable at one step separate under geometric composition and identifies the finite composition scale at which chaos emerges. We use this mechanism to establish a new form of global chaos control: minute phase actions reorient the successive non-normal amplification directions so that their geometric composition becomes contracting, suppressing chaos at fixed dissipation without reducing local amplification or targeting a preselected orbit.

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Cite

BibTeXRIS
BibTeX
@misc{sornette2026route,
  title = {{A New Route to Chaos through the Geometric Composition of Non-Normal Amplification}},
  author = {D. Sornette and V. R. Saiprasad and V. Troude},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.18017},
  eprint = {2609.18017},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.18017},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A New Route to Chaos through the Geometric Composition of Non-Normal Amplification
AU  - D. Sornette
AU  - V. R. Saiprasad
AU  - V. Troude
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.18017
UR  - https://arxiv.org/abs/2609.18017
AB  - Chaos emerges when stretching is repeatedly recycled by reinjection. We uncover a new route to chaos in which the decisive variable is the temporal order of non-normal tangent maps: periodic and chaotic states can share essentially the same one-step stretching statistics while their ordered products acquire opposite Lyapunov growth. We introduce the ordered-product growth rate h_L over L successive tangent maps, which reveals how states indistinguishable at one step separate under geometric composition and identifies the finite composition scale at which chaos emerges. We use this mechanism to establish a new form of global chaos control: minute phase actions reorient the successive non-normal amplification directions so that their geometric composition becomes contracting, suppressing chaos at fixed dissipation without reducing local amplification or targeting a preselected orbit.
ER  -