On the Partial Hyperbolicity of Robustly Transitive Sets with Singularities
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Dynamics and Differential Equations"
DOI: 10.1007/s10884-022-10132-7
Abstract: Homoclinic tangencies and singular hyperbolicity are involved in the Palis conjecture for vector fields. Typical three dimensional vector fields are well understood by recent works. We study the dynamics of higher dimensional vector fields that… read more here.
Keywords: robustly transitive; homoclinic tangencies; dimensional vector; vector fields ... See more keywords
On the notions of singular domination and (multi-)singular hyperbolicity
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DOI: 10.1007/s11425-019-1764-x
Abstract: The properties of uniform hyperbolicity and dominated splitting have been introduced to study the stability of the dynamics of diffeomorphisms. One meets difficulties when one tries to extend these definitions to vector fields and Shantao… read more here.
Keywords: hyperbolicity; multi singular; singular hyperbolicity; singular domination ... See more keywords
A characterization of singular hyperbolicity via the linear Poincaré flow
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DOI: 10.1016/j.jde.2019.10.029
Abstract: Abstract Singular hyperbolicity is a fundamental notion in dynamical systems that describes in particular Lorenz-like dynamics. It is defined using the tangent flow and concerns both the regular and singular parts of the dynamics. In… read more here.
Keywords: singular hyperbolicity; hyperbolicity via; characterization singular; hyperbolicity ... See more keywords
The weak Smale horseshoe and mean hyperbolicity
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DOI: 10.1016/j.jde.2021.07.020
Abstract: Abstract The paper concerns the mean hyperbolicity of the skew-product flows induced by the perturbation equations driven by varieties of non-periodic forcings. The weakly averaged horseshoe can be constructed as a mean hyperbolic invariant set… read more here.
Keywords: hyperbolicity; mean hyperbolicity; smale horseshoe; horseshoe mean ... See more keywords
Cosmic voids and induced hyperbolicity
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DOI: 10.1140/epjp/s13360-020-00963-y
Abstract: Cosmic voids—the low density regions in the Universe—as characteristic features of the large-scale matter distribution, are known for their hyperbolic properties. The latter implies the deviation of photon beams due to their underdensity, thus mimicing… read more here.
Keywords: hyperbolicity; voids induced; cosmic voids; induced hyperbolicity ... See more keywords
Hyperbolicity of First Order Quasi-Linear Equations
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DOI: 10.3390/sym14051024
Abstract: The theorem about equivalence of the strong hyperbolicity concept and the Friedrichs hyperbolicity concept for partial quasi-linear differential equations of the first order is proved. On the basis of this theorem, the necessary and sufficient… read more here.
Keywords: first order; hyperbolicity first; hyperbolicity; quasi linear ... See more keywords