Issue |
Europhys. Lett.
Volume 47, Number 6, September II 1999
|
|
---|---|---|
Page(s) | 649 - 655 | |
Section | General | |
DOI | https://doi.org/10.1209/epl/i1999-00438-4 | |
Published online | 01 September 2002 |
Nonlinear dependencies between sets of periodic orbits
Departamento de Física, Faculdade de Ciências, Universidade de Lisboa 1749-016 Lisboa, Portugal Instituto de Física, Universidade Federal do Rio Grande do Sul 91501-970 Porto Alegre, Brazil
Received:
20
May
1999
Accepted:
19
July
1999
We report the existence of a phenomenon of inheritance
among periodic trajectories of the quadratic map.
Within the set of all possible trajectories of period
k we find "mother” trajectories from which several
"daughters” may be derived by simple polynomial
transformations.
For example, from the six orbital points zi of a period-six
mother we get three additional period-six daughters as the
zeros of the six cubics
.
Daughters might have daughters.
This stratification shows that periodic orbits are not necessarily
independent of each other.
This fact could be of importance for decomposing certain sums
involving sets of periodic trajectories,
particularly for trace formulas underlying semiclassical interpretations
of spectra in atomic physics.
PACS: 05.45.-a – Nonlinear dynamics and nonlinear dynamical systems / 45.05.+x – General theory of classical mechanics of discrete systems / 03.65.Fd – Algebraic methods
© EDP Sciences, 1999
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.