Bundle switching in higher dimensions
Andy Hammerlindl

TL;DR
This paper explores how certain three-dimensional dynamical systems can be extended to higher dimensions, resulting in new examples of partially hyperbolic diffeomorphisms that are dynamically incoherent, with implications for understanding complex dynamical behaviors.
Contribution
It introduces a method to construct higher-dimensional partially hyperbolic diffeomorphisms from three-dimensional systems, demonstrating the occurrence of dynamical incoherence in these higher-dimensional cases.
Findings
Construction of 4D dynamically incoherent partially hyperbolic diffeomorphisms from 3D systems
Extension of results to higher dimensions under additional assumptions
Identification of conditions preserving orientation of stable bundles
Abstract
Assuming it preserves an orientation of its stable bundle, any three-dimensional partially hyperbolic diffeomorphism can be used to construct a four-dimensional partially hyperbolic diffeomorphism which is dynamically incoherent. Under the same assumption, the time-one map of any three-dimensional Anosov flow can be used to construct a four-dimensional diffeomorphism which is both absolutely partially hyperbolic and dynamically incoherent. Further results hold in higher dimensions under additional assumptions.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Quantum chaos and dynamical systems · Nonlinear Dynamics and Pattern Formation
