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.

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.

Periodic points and topological entropy of one dimensional maps

1980 ◽  
pp. 18-34 ◽  
Author(s):  
Louis Block ◽  
John Guckenheimer ◽  
Michal Misiurewicz ◽  
Lai Sang Young
Keyword(s):  
Topological Entropy ◽  
Periodic Points ◽  
One Dimensional ◽  
One Dimensional Maps

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 ${\mathcal{F}}$.

scholarly journals The chain recurrent set, attractors, and explosions

1985 ◽  
Vol 5 (3) ◽  
pp. 321-327 ◽  
Author(s):  
Louis Block ◽  
John E. Franke
Keyword(s):  
Compact Space ◽  
Metric Space ◽  
Periodic Points ◽  
Limit Set ◽  
Compact Metric Space ◽  
Continuous Map ◽  
Special Case ◽  
Equivalent Conditions ◽  
Chain Recurrent Set ◽  
Recurrent Set

AbstractCharles Conley has shown that for a flow on a compact metric space, a point x is chain recurrent if and only if any attractor which contains the & ω-limit set of x also contains x. In this paper we show that the same statement holds for a continuous map of a compact metric space to itself, and additional equivalent conditions can be given. A stronger result is obtained if the space is locally connected.It follows, as a special case, that if a map of the circle to itself has no periodic points then every point is chain recurrent. Also, for any homeomorphism of the circle to itself, the chain recurrent set is either the set of periodic points or the entire circle. Finally, we use the equivalent conditions mentioned above to show that for any continuous map f of a compact space to itself, if the non-wandering set equals the chain recurrent set then f does not permit Ω-explosions. The converse holds on manifolds.

Properties of attractors of generic homeomorphisms

1996 ◽  
Vol 16 (6) ◽  
pp. 1297-1310 ◽  
Author(s):  
Mike Hurley
Keyword(s):  
Periodic Points ◽  
Compact Manifolds ◽  
Generic Properties ◽  
Chain Recurrent Set ◽  
Recurrent Set

AbstractWe describe several generic properties of homeomorphisms on compact manifolds. These properties concern the attractors of a homeomorphism, its chain recurrent set, and the periodic points.

Characterization of Minimum Route MTM in One-Dimensional Multi-Hop Wireless Networks

2009 ◽  
Vol E92-A (9) ◽  
pp. 2227-2235 ◽  
Author(s):  
Kazuyuki MIYAKITA ◽  
Keisuke NAKANO ◽  
Masakazu SENGOKU ◽  
Shoji SHINODA
Keyword(s):  
Wireless Networks ◽  
One Dimensional

Solvothermal Synthesis and Characterization of an One-Dimensional Zinc Phosphate

2002 ◽  
Vol 37 (2-3) ◽  
pp. 169-175 ◽  
Author(s):  
K. Yanxiong ◽  
L. Jianmin ◽  
Z. Yugen ◽  
H. Gaofei ◽  
J. Zheng ◽  
...  
Keyword(s):  
Solvothermal Synthesis ◽  
Zinc Phosphate ◽  
Synthesis And Characterization ◽  
One Dimensional

scholarly journals Synthesis and Structural Characterization of (E)-4-[(2-Hydroxy-3-methoxybenzylidene)amino]butanoic Acid and Its Novel Cu(II) Complex

Molbank ◽  
10.3390/m1179 ◽  
2021 ◽  
Vol 2021 (1) ◽  
pp. M1179
Author(s):  
Eleftherios Halevas ◽  
Antonios Hatzidimitriou ◽  
Barbara Mavroidi ◽  
Marina Sagnou ◽  
Maria Pelecanou ◽  
...  
Keyword(s):  
Schiff Base ◽  
Gamma Aminobutyric Acid ◽  
X Ray Diffraction ◽  
Reaction Conditions ◽  
Polymeric Compound ◽  
Bridging Ligands ◽  
1H And 13C Nmr ◽  
One Dimensional ◽  
Ft Ir

A novel Cu(II) complex based on the Schiff base obtained by the condensation of ortho-vanillin with gamma-aminobutyric acid was synthesized. The compounds are physico-chemically characterized by elemental analysis, HR-ESI-MS, FT-IR, and UV-Vis. The complex and the Schiff base ligand are further structurally identified by single crystal X-ray diffraction and 1H and 13C-NMR, respectively. The results suggest that the Schiff base are synthesized in excellent yield under mild reaction conditions in the presence of glacial acetic acid and the crystal structure of its Cu(II) complex reflects an one-dimensional polymeric compound. The molecular structure of the complex consists of a Cu(II) ion bound to two singly deprotonated Schiff base bridging ligands that form a CuN2O4 chelation environment, and a coordination sphere with a disordered octahedral geometry.

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