We study one-parameter families of quasi-periodically forced monotone interval maps and provide sufficient conditions for the existence of a parameter at which the respective system possesses a non-uniformly hyperbolic attractor. This is equivalent to the existence of a sink-source orbit, that is, an orbit with positive Lyapunov exponent both forwards and backwards in time. The attractor itself is a non-continuous invariant graph with negative Lyapunov exponent, often referred to as ‘SNA’. In contrast to former results in this direction, our conditions are C² -open in the fibre maps. By applying a general result about saddle-node bifurcations in skew-products, we obtain a conclusion on the occurrence of non-smooth bifurcations in the respective families. Explicit examples show the applicability of the derived statements.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:70707 |
| Date | 03 June 2020 |
| Creators | Fuhrmann, Gabriel |
| Publisher | Cambridge University Press |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:article, info:eu-repo/semantics/article, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | 0143-3857, 1469-4417, 10.1017/etds.2014.92, info:eu-repo/grantAgreement/German Research Council/Emmy-Noether-grant/ Ja 1721/2-1//Low-dimensional and Nonautonomous Dynamics |
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