Persistent heterodimensional cycles in periodic perturbations of Lorenz-like attractors

@article{Li2017PersistentHC,
  title={Persistent heterodimensional cycles in periodic perturbations of Lorenz-like attractors},
  author={Dongchen Li and Dmitry Turaev},
  journal={arXiv: Dynamical Systems},
  year={2017}
}
We prove that heterodimensional cycles can be created by unfolding a pair of homoclinic tangencies in a certain class of C-infinity diffeomorphisms. This implies the existence of a C2- open domain in the space of dynamical systems with a certain type of symmetry where systems with heterodimensional cycles are dense in C-infinity. In particular, we describe a class of three-dimensional flows with a Lorenz-like attractor such that an arbitrarily small perturbation of any such flow can belong to… Expand

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TLDR
It is shown that the impossibility of giving a finite-parameter complete description of dynamics and bifurcations of the quasiattractors of so-called quasiattraction systems may exhibit rather non-trivial features which are in a sharp distinction with that one could expect in analogy with hyperbolic or Lorenz-like attractors. Expand
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