Quick Navigation

Overview Topics Abstract Importance Paper Tools References Reactions Discussion Publication Related

Topics

Open Quantum Systems Decoherence Quantum Simulation

Infinite hierarchies of nonlinearly dependent periodic orbits.

PubMed
Authors: Gallas JA

Year

2001

Paper ID

13234

Status

Peer-reviewed

Abstract Read

~2 min

Abstract Words

85

Citations

11

Abstract

Quadratic maps are used to show explicitly that the skeleton of unstable periodic orbits underlying classical and quantum dynamics is stratified into a doubly infinite hierarchy of orbits inherited from a set of basic "seeds" through certain nonlinear transformations T(alpha)(x). The hierarchy contains nonunique substructurings which arise from the different possibilities of sequencing the transformations T(alpha)(x). The structuring of the orbital skeleton is shown to be generic for Abelian equations, i.e., for all dynamical systems generated by iterating rational functions.

Why This Paper Matters

  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
  • It adds a 2001 reference point for readers tracking recent quantum research.
  • Quadratic maps are used to show explicitly that the skeleton of unstable periodic orbits underlying classical and quantum dynamics is stratified into a doubly infinite...

Paper Tools

Become a member to use research tools

Sign in to open papers, visit source links, share, cite, compare, copy DOI links, request category corrections, and build your reading list.

Become a member Sign in
Publisher Share Cite This Paper Copy URL Compare Copy DOI Add to Reading List Category Correction Request

References & Citation Signals

[1] DOI https://doi.org/10.1103/PhysRevE.63.016216 [2] Publisher https://pubmed.ncbi.nlm.nih.gov/11304344/

Local Citation Graph (Related-Paper Links)

Current Paper #13234 #68456 Analytic Properties of the Jost... #68455 Mediative Fuzzy Logic: From Typ... #68453 Weak wave turbulence as a precu... #68437 Transition-state lattice modes ...

External citation index: OpenAlex citation signal • updated 2026-06-13 04:49:50

Community Reactions

Quick sentiment from readers on this paper.

Score: 0
Likes: 0 Dislikes: 0

Sign in to react to this paper.

Discussion & Reviews (Moderated)

Average Rating: 0.0 / 5 (0 ratings)

No written reviews yet.