The bifurcation of periodic orbits and equilibrium points in the linked restricted three-body problem with parameter <i>ω</i>
Bibliographic record
Abstract
This paper is devoted to the bifurcation of periodic orbits and libration points in the linked restricted three-body problem (LR3BP). Inherited from the classic circular restricted three-body problem (CR3BP), it retains most of the dynamical structure of CR3BP, while its dynamical flow is dominated by angular velocity ω and Jacobi energy C. Thus, for the first time, the influence of the angular velocity in the three-body problem is discussed in this paper based on ω-motivated and C-motivated bifurcation. The existence and collision of equilibrium points in the LR3BP are investigated analytically. The dynamic bifurcation of the LR3BP under angular velocity variation is obtained based on three typical kinds of periodic orbits, i.e., planar and vertical Lyapunov orbits and Halo orbits. More bifurcation points are supplemented to Doedel's results in the CR3BP for a global sketch of bifurcation families. For the first time, a new bifurcation phenomenon is discovered that as ω approaches to 1.4, two period-doubling bifurcation points along the Halo family merge together. It suggests that the number and the topological type of bifurcation points themselves can be altered when the system parameter varies in LR3BP. Thus, it is named as “bifurcation of bifurcation” or “secondary bifurcation” in this paper. At selected values of ω, the phase space structures of equilibrium points L2 and L3 are revealed by Lie series method numerically, presenting the center manifolds on the Poincaré section and detecting three patterns of evolution for center manifolds in LR3BP.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".