| Title:
|
Computing the differential of an unfolded contact diffeomorphism (English) |
| Author:
|
Böhmer, Klaus |
| Author:
|
Janovská, Drahoslava |
| Author:
|
Janovský, Vladimír |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
48 |
| Issue:
|
1 |
| Year:
|
2003 |
| Pages:
|
3-30 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Consider a bifurcation problem, namely, its bifurcation equation. There is a diffeomorphism $\Phi $ linking the actual solution set with an unfolded normal form of the bifurcation equation. The differential $D\Phi (0)$ of this diffeomorphism is a valuable information for a numerical analysis of the imperfect bifurcation. The aim of this paper is to construct algorithms for a computation of $D\Phi (0)$. Singularity classes containing bifurcation points with $\mathop {\mathrm codim}\le 3$, $\mathop {\mathrm corank}=1$ are considered. (English) |
| Keyword:
|
bifurcation points |
| Keyword:
|
imperfect bifurcation diagrams |
| Keyword:
|
qualitative analysis |
| MSC:
|
34A34 |
| MSC:
|
35B32 |
| MSC:
|
37C05 |
| MSC:
|
47J15 |
| MSC:
|
58K20 |
| MSC:
|
65L99 |
| MSC:
|
65P30 |
| idZBL:
|
Zbl 1099.34007 |
| idMR:
|
MR1954501 |
| DOI:
|
10.1023/A:1022950819918 |
| . |
| Date available:
|
2009-09-22T18:12:00Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134514 |
| . |
| Reference:
|
[1] K. Böhmer: On a numerical Lyapunov-Schmidt method for operator equations.Computing 53 (1993), 237–269. MR 1253405 |
| Reference:
|
[2] K. Böhmer, D. Janovská and V. Janovský: Computer aided analysis of the imperfect bifurcation diagrams.East-West J. Numer. Math. (1998), 207–222. MR 1652813 |
| Reference:
|
[3] K. Böhmer, D. Janovská and V. Janovský: On the numerical analysis of the imperfect bifurcation.SIAM J. Numer. Anal. 40 (2002), 416–430. MR 1921663, 10.1137/S0036142900369283 |
| Reference:
|
[4] S. N. Chow, J. Hale: Methods of Bifurcation Theory.Springer Verlag, New York, 1982. MR 0660633 |
| Reference:
|
[5] M. Golubitsky, D. Schaeffer: A theory for imperfect bifurcation via singularity theory.Commun. Pure Appl. Math. 32 (1979), 21–98. MR 0508917, 10.1002/cpa.3160320103 |
| Reference:
|
[6] M. Golubitsky, D. Schaeffer: Singularities and Groups in Bifurcation Theory, Vol. 1.Springer Verlag, New York, 1985. MR 0771477 |
| Reference:
|
[7] W. Govaerts: Numerical Methods for Bifurcations of Dynamical Equilibria.SIAM, Philadelphia, 2000. Zbl 0935.37054, MR 1736704 |
| Reference:
|
[8] V. Janovský, P. Plecháč: Computer aided analysis of imperfect bifurcation diagrams I. Simple bifurcation point and isola formation centre.SIAM J. Num. Anal. 21 (1992), 498-512. MR 1154278 |
| . |
