Abstract
We investigate the structure of Arnol’d tongues passing through a quasi-periodic saddle-node bifurcation in a 3D map. Due to resonances, the bifurcation set has a complicated structure. Using numerical continuation in MatcontM and Lyapunov exponents we explore the tongues and the quasi-periodic saddle-node bifurcation set.
The bifurcation set emerges from two Chenciner bifurcations. Both sets terminate in a homoclinic bifurcation of a neutral saddle cycle of period 3. It is similar to a case for vector fields, but the first report of such a codim-2 homoclinic tangency bifurcation in a map. We also show how these manifolds oscillate around the saddle near the tangency, for real and complex multipliers.
The bifurcation set emerges from two Chenciner bifurcations. Both sets terminate in a homoclinic bifurcation of a neutral saddle cycle of period 3. It is similar to a case for vector fields, but the first report of such a codim-2 homoclinic tangency bifurcation in a map. We also show how these manifolds oscillate around the saddle near the tangency, for real and complex multipliers.
| Original language | English |
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| Title of host publication | Proceedings of the 9th European Nonlinear Dynamics Conference |
| Editors | Gábor Stépán, Gábor Csernák |
| Place of Publication | Budapest |
| Publisher | CongressLIne Ltd. |
| Number of pages | 2 |
| ISBN (Electronic) | 978-963-12-9168-1 |
| Publication status | Published - 2017 |
| Event | 9th European Nonlinear Dynamics Conference - Budapest University of Technology end Economics, Budapest, Hungary Duration: 25 Jun 2017 → 30 Jun 2017 Conference number: 9 |
Conference
| Conference | 9th European Nonlinear Dynamics Conference |
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| Abbreviated title | ENOC 2017 |
| Country/Territory | Hungary |
| City | Budapest |
| Period | 25/06/17 → 30/06/17 |