Shadowing, thick sets and the Ramsey property

2015 ◽  
Vol 36 (5) ◽  
pp. 1582-1595 ◽  
Author(s):  
PIOTR OPROCHA
Keyword(s):  
Arbitrary Sequence ◽  
Ramsey Property ◽  
Shadowing Property ◽  
Full Characterization ◽  
Equivalent Properties ◽  
Chain Recurrent Set ◽  
Recurrent Set

We provide a full characterization of relations between the shadowing property and the thick shadowing property. We prove that they are equivalent properties for non-wandering systems, the thick shadowing property is always a consequence of the shadowing property, and the thick shadowing property on the chain-recurrent set and the thick shadowing property are the same properties. We also provide a full characterization of the cases when for any family ${\mathcal{F}}$ with the Ramsey property an arbitrary sequence of points can be ${\it\varepsilon}$-traced over a set from ${\mathcal{F}}$.

SIMPLE AND COMPLEX DYNAMICS FOR ONE-DIMENSIONAL MANIFOLD MAPS

1995 ◽  
Vol 05 (05) ◽  
pp. 1351-1355
Author(s):  
VLADIMIR FEDORENKO
Keyword(s):  
Topological Entropy ◽  
Complex Dynamics ◽  
Periodic Points ◽  
Dimensional Manifold ◽  
One Dimensional ◽  
Circle Maps ◽  
Interval Maps ◽  
Chain Recurrent Set ◽  
Recurrent Set

We give a characterization of complex and simple interval maps and circle maps (in the sense of positive or zero topological entropy respectively), formulated in terms of the description of the dynamics of the map on its chain recurrent set. We also describe the behavior of complex maps on their periodic points.

Chain transitivity and variations of the shadowing property

2014 ◽  
Vol 35 (7) ◽  
pp. 2044-2052 ◽  
Author(s):  
WILLIAM R. BRIAN ◽  
JONATHAN MEDDAUGH ◽  
BRIAN E. RAINES
Keyword(s):  
Arbitrary Sequence ◽  
Ramsey Property ◽  
Shadowing Property ◽  
Chain Transitivity ◽  
A Chain

We show that, under the assumption of chain transitivity, the shadowing property is equivalent to the thick shadowing property. We also show that, if ${\mathcal{F}}$ is a family with the Ramsey property, then an arbitrary sequence of points in a chain transitive space can be ${\it\varepsilon}$-shadowed (for any ${\it\varepsilon}$) on a set in ${\mathcal{F}}$.

Partially hyperbolic diffeomorphisms with a uniformly compact center foliation: the quotient dynamics

2015 ◽  
Vol 36 (4) ◽  
pp. 1067-1105 ◽  
Author(s):  
DORIS BOHNET ◽  
CHRISTIAN BONATTI
Keyword(s):  
Quotient Space ◽  
Shadowing Property ◽  
Hyperbolic Diffeomorphisms ◽  
Partially Hyperbolic ◽  
Partially Hyperbolic Diffeomorphisms ◽  
Chain Recurrent Set ◽  
Recurrent Set

We show that a partially hyperbolic $C^{1}$-diffeomorphism $f:M\rightarrow M$ with a uniformly compact $f$-invariant center foliation ${\mathcal{F}}^{c}$ is dynamically coherent. Further, the induced homeomorphism $F:M/{\mathcal{F}}^{c}\rightarrow M/{\mathcal{F}}^{c}$ on the quotient space of the center foliation has the shadowing property, i.e. for every ${\it\epsilon}>0$ there exists ${\it\delta}>0$ such that every ${\it\delta}$-pseudo-orbit of center leaves is ${\it\epsilon}$-shadowed by an orbit of center leaves. Although the shadowing orbit is not necessarily unique, we prove the density of periodic center leaves inside the chain recurrent set of the quotient dynamics. Other interesting properties of the quotient dynamics are also discussed.

scholarly journals The generalized recurrent set and strong chain recurrence

2016 ◽  
Vol 38 (2) ◽  
pp. 788-800 ◽  
Author(s):  
JIM WISEMAN
Keyword(s):  
Chain Recurrence ◽  
Chain Recurrent Set ◽  
Recurrent Set

Fathi and Pageault have recently shown a connection between Auslander’s generalized recurrent set$\text{GR}(f)$and Easton’s strong chain recurrent set. We study$\text{GR}(f)$by examining that connection in more detail, as well as connections with other notions of recurrence. We give equivalent definitions that do not refer to a metric. In particular, we show that$\text{GR}(f^{k})=\text{GR}(f)$for any$k>0$, and give a characterization of maps for which the generalized recurrent set is different from the ordinary chain recurrent set.

A Thorough Theoretical Exploration of Intriguing Characteristics of Cyclo[18]carbon: Geometry, Bonding Nature, Aromaticity, Weak Interaction, Reactivity, Excited States, Vibrations, Molecular Dynamics and Various Molecular Properties

2019 ◽  
Author(s):  
Tian Lu ◽  
Qinxue Chen ◽  
Zeyu Liu
Keyword(s):  
Molecular Dynamics ◽  
Excited States ◽  
Electronic Excitation ◽  
Ring Structure ◽  
Molecular Properties ◽  
Molecular Vibration ◽  
Full Characterization ◽  
Long Time ◽  
Almost All

Although cyclo[18]carbon has been theoretically and experimentally investigated since long time ago, only very recently it was prepared and directly observed by means of STM/AFM in condensed phase (Kaiser et al., <i>Science</i>, <b>365</b>, 1299 (2019)). The unique ring structure and dual 18-center π delocalization feature bring a variety of unusual characteristics and properties to the cyclo[18]carbon, which are quite worth to be explored. In this work, we present an extremely comprehensive and detailed investigation on almost all aspects of the cyclo[18]carbon, including (1) Geometric characteristics (2) Bonding nature (3) Electron delocalization and aromaticity (4) Intermolecular interaction (5) Reactivity (6) Electronic excitation and UV/Vis spectrum (7) Molecular vibration and IR/Raman spectrum (8) Molecular dynamics (9) Response to external field (10) Electron ionization, affinity and accompanied process (11) Various molecular properties. We believe that our full characterization of the cyclo[18]carbon will greatly deepen researchers' understanding of this system, and thereby help them to utilize it in practice and design its various valuable derivatives.

A Thorough Theoretical Exploration of Intriguing Characteristics of Cyclo[18]carbon: Geometry, Bonding Nature, Aromaticity, Weak Interaction, Reactivity, Excited States, Vibrations, Molecular Dynamics and Various Molecular Properties

2019 ◽  
Author(s):  
Tian Lu ◽  
Qinxue Chen ◽  
Zeyu Liu
Keyword(s):  
Molecular Dynamics ◽  
Excited States ◽  
Electronic Excitation ◽  
Ring Structure ◽  
Molecular Properties ◽  
Molecular Vibration ◽  
Full Characterization ◽  
Long Time ◽  
Almost All

Although cyclo[18]carbon has been theoretically and experimentally investigated since long time ago, only very recently it was prepared and directly observed by means of STM/AFM in condensed phase (Kaiser et al., <i>Science</i>, <b>365</b>, 1299 (2019)). The unique ring structure and dual 18-center π delocalization feature bring a variety of unusual characteristics and properties to the cyclo[18]carbon, which are quite worth to be explored. In this work, we present an extremely comprehensive and detailed investigation on almost all aspects of the cyclo[18]carbon, including (1) Geometric characteristics (2) Bonding nature (3) Electron delocalization and aromaticity (4) Intermolecular interaction (5) Reactivity (6) Electronic excitation and UV/Vis spectrum (7) Molecular vibration and IR/Raman spectrum (8) Molecular dynamics (9) Response to external field (10) Electron ionization, affinity and accompanied process (11) Various molecular properties. We believe that our full characterization of the cyclo[18]carbon will greatly deepen researchers' understanding of this system, and thereby help them to utilize it in practice and design its various valuable derivatives.

scholarly journals Full Characterization of Minimal Linear Codes as Cutting Blocking Sets

2021 ◽  
pp. 1-1
Author(s):  
Chunming Tang ◽  
Yan Qiu ◽  
Qunying Liao ◽  
Zhengchun Zhou
Keyword(s):  
Linear Codes ◽  
Blocking Sets ◽  
Full Characterization

scholarly journals Special Issue: Advances in Computational Electromagnetics

2021 ◽  
Vol 7 (6) ◽  
pp. 89
Author(s):  
Valerio De Santis
Keyword(s):  
Rare Earth ◽  
Magnetic Materials ◽  
Permanent Magnets ◽  
Computational Electromagnetics ◽  
Superconducting Materials ◽  
Special Issue ◽  
Full Characterization ◽  
Recent Advances

Recent advances in computational electromagnetics (CEMs) have made the full characterization of complex magnetic materials possible, such as superconducting materials, composite or nanomaterials, rare-earth free permanent magnets, etc [...]

scholarly journals Full characterization of the transmission properties of a multi-plane light converter

2021 ◽  
Vol 3 (2) ◽  
Author(s):  
Pauline Boucher ◽  
Arthur Goetschy ◽  
Giacomo Sorelli ◽  
Mattia Walschaers ◽  
Nicolas Treps
Keyword(s):  
Full Characterization ◽  
Transmission Properties ◽  
Plane Light
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