Kaszás Bálint, Feudel Ulrike, Tél Tamás
Institute for Theoretical Physics, Eötvös Loránd University, Pázmány Péter Sétány 1/A, H-1117 Budapest, Hungary.
Theoretical Physics/Complex Systems, ICBM, Carl von Ossietzky University Oldenburg, 26129 Oldenburg, Germany.
Chaos. 2018 Mar;28(3):033612. doi: 10.1063/1.5013336.
Our aim is to unfold phase space structures underlying systems with a drift in their parameters. Such systems are non-autonomous and belong to the class of non-periodically driven systems where the traditional theory of chaos (based e.g., on periodic orbits) does not hold. We demonstrate that even such systems possess an underlying topological horseshoe-like structure at least for a finite period of time. This result is based on a specifically developed method which allows to compute the corresponding time-dependent stable and unstable foliations. These structures can be made visible by prescribing a certain type of history for an ensemble of trajectories in phase space and by analyzing the trajectories fulfilling this constraint. The process can be considered as a leaking in history space-a generalization of traditional leaking, a method that has become widespread in traditional chaotic systems, to leaks depending on time.
