BANERJEE, SOUMITRO ; GIAOURIS, DAMIAN ; MISSAILIDIS, PETROS ; IMRAYED, OTMAN (2012) LOCAL BIFURCATIONS OF A QUASIPERIODIC ORBIT International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 22 (12). p. 1250289. ISSN 0218-1274
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Official URL: http://doi.org/10.1142/S0218127412502896
Related URL: http://dx.doi.org/10.1142/S0218127412502896
Abstract
We consider the local bifurcations that can occur in a quasiperiodic orbit in a three-dimensional map: (a) a torus doubling resulting in two disjoint loops, (b) a torus doubling resulting in a single closed curve with two loops, (c) the appearance of a third frequency, and (d) the birth of a stable torus and an unstable torus. We analyze these bifurcations in terms of the stability of the point at which the closed invariant curve intersects a "second Poincaré section". We show that these bifurcations can be classified depending on where the eigenvalues of this fixed point cross the unit circle.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to World Scientific Publishing Company. |
| ID Code: | 129532 |
| Deposited On: | 17 Nov 2022 06:56 |
| Last Modified: | 17 Nov 2022 06:56 |
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