We show that if a volume-preserving diffeomorphism belongs to the C1-interior of the set of all volume preserving diffeomorphisms having the periodic shadowing property then it is Anosov. Mathematics Subject Classification: 37C10, 37C50, 37D20

In this work we study the problem of positiveness topological entropy for flows using pointwise dynamics. We show that existence a non-periodic nonwandering point an expansive and non-singular flow with shadowing is sufficient condition to obtain positive entropy. Moreover, can deal singularities, showing non-wandering, non-critical, strongly-shadowable, uniform-expansive implies symbolic subsh...

A standard use of shadowing lemmas in dynamical systems theory is to prove density of periodic points. When there is symmetry present it is natural to investigate the density of periodic points of a given symmetry. We obtain several results in this direction. As an application, we prove a result about compact group extensions of hyperbolic and nonuniformly hyperbolic dynamical systems.

Infinite population models of co-evolutionary dynamics are useful mathematical constructs hinting at the possibility of a wide variety of possible dynamical regimes from simple attractive fixed point behavior, periodic orbits to complex chaotic dynamics. We propose to use the framework of shadowing lemma to link such mathematical constructs to large finite population computer simulations. We al...

Stray light is a known strong interference in spectroscopic measurements. Photons from high-intensity signals that are scattered inside the spectrometer, or photons enter detector through unintended ways, will be added to spectrum as an signal. A general experimental solution this problem presented here by introducing customized fiber for signal collection. The fiber-mount spectrometer consists...

Scaffolding and shadowing techniques have been shown to improve language learners’ reading comprehension. However, little attention has been paid to the comparative effectiveness of these techniques. This study investigated the effect of three selected scaffolding techniques (peer scaffolding, distributed scaffolding, and reciprocal scaffolding) versus three types of shadowing (complete shadowi...