Special Issue "Shadowing in Dynamical Systems"
Deadline for manuscript submissions: closed (31 May 2019) | Viewed by 8875
Interests: shadowing property; dynamical systems theory; bifurcation theory; ergodic theory; vector fields; chaos theory
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Since Anosov and Bowen's works, the notion of pseudo-orbits very often appears in several branches of the modern theory of dynamical systems, and, especially, the pseudo-orbits shadowing property (in what follows, this is called the shadowing property) usually plays an important part, not only in the numerical study of dynamical systems, but also in the qualitative study of dynamical systems. In fact, the shadowing property has been applied to the modern theory of structural stability and has played one of the main roles in the global theory of dynamical systems. The shadowing theory of dynamical systems is now an important and rapidly developing branch of the mordern theory of dynamical systems.
Various types of shadowing properties have been introduced in the literature since Anosov and Bowen's works, and, nowadays, these notions are intensively studied by many authors in the platform of topological dynamical systems. Many essential and interesting results have been obtained from the view point of, for instance, measure theory, chaos theory, and combinatorics.
In this Special Issue, by collecting recent achievements on the shadowing property from the dynamical systems community around the world, we would like to spur the study of shadowing theory to explore the new directions and further developments in the theory.
In this issue, we particularly seek contributions on the following three topics:
- new results on the shadowing property in the frameworks of uniformly hyperbolic systems, non-uniformly hyperbolic systems and topological dynamical systems
- new results on the shadowing property intertwined with bifurcation theory, ergodic theory, and so on.
- survey articles which present significant (new or not so new) open questions.
Prof. Dr. Kazuhiro Sakai
Manuscript Submission Information
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- shadowing property
- average shadowing property
- limit shadowing property
- weak shadowing property
- orbital shadowing property
- shadowing measures
- topologically stable
- uniformly hyperbolic and non-uniformly hyperbolic
- dominated splittings
- singular hyperbolic
- continuum-wise expansive
- expansive measures
- bifurcation theory
- ergodic theory
- chaos theory