scholarly journals Continuous curves of nonmetric pseudo-arcs and semi-conjugacies to interval maps

2020 ◽  
Vol 282 ◽  
pp. 107309
Author(s):  
Jan P. Boroński ◽  
Michel Smith
Keyword(s):  
Interval Maps ◽  
Continuous Curves

TEM Analysis of Long-Period Polytypes in SiC—S

1976 ◽  
Vol 34 ◽  
pp. 630-631
Author(s):  
S. Shinozaki ◽  
J. W. Sprys
Keyword(s):  
Electron Diffraction ◽  
Isothermal Annealing ◽  
Tem Analysis ◽  
Long Period ◽  
Transmission Electron ◽  
Average Grain Size ◽  
High Resolution Tem ◽  
Structural Lattice ◽  
The Stability ◽  
Continuous Curves

In reaction sintered SiC (∽ 5um average grain size), about 15% of the grains were found to have long-period structures, which were identifiable by transmission electron microscopy (TEM). In order to investigate the stability of the long-period polytypes at high temperature, crystal structures as well as microstructural changes in the long-period polytypes were analyzed as a function of time in isothermal annealing.Each polytype was analyzed by two methods: (1) Electron diffraction, and (2) Electron micrograph analysis. Fig. 1 shows microdensitometer traces of ED patterns (continuous curves) and calculated intensities (vertical lines) along 10.l row for 6H and 84R (Ramsdell notation). Intensity distributions were calculated based on the Zhdanov notation of (33) for 6H and [ (33)3 (32)2 ]3 for 84R. Because of the dynamical effect in electron diffraction, the observed intensities do not exactly coincide with those intensities obtained by structure factor calculations. Fig. 2 shows the high resolution TEM micrographs, where the striped patterns correspond to direct resolution of the structural lattice periodicities of 6H and 84R structures and the spacings shown in the figures are as expected for those structures.

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.

UNIMODAL INTERVAL MAPS OBTAINED FROM THE MODIFIED CHUA EQUATIONS

1993 ◽  
Vol 03 (02) ◽  
pp. 323-332 ◽  
Author(s):  
MICHAŁ MISIUREWICZ
Keyword(s):  
Periodic Orbit ◽  
Critical Point ◽  
Real Line ◽  
Positive Measure ◽  
Schwarzian Derivative ◽  
Large Range ◽  
Unimodal Maps ◽  
Interval Maps ◽  
Central Piece ◽  
Piecewise Continuous

Following Brown [1992, 1993] we study maps of the real line into itself obtained from the modified Chua equations. We fix our attention on a one-parameter family of such maps, which seems to be typical. For a large range of parameters, invariant intervals exist. In such an invariant interval, the map is piecewise continuous, with most of pieces of continuity mapped in a monotone way onto the whole interval. However, on the central piece there is a critical point. This allows us to find sometimes a smaller invariant interval on which the map is unimodal. In such a way, we get one-parameter families of smooth unimodal maps, very similar to the well-known family of logistic maps x ↦ ax(1−x). We study more closely one of those and show that these maps have negative Schwarzian derivative. This implies the existence of at most one attracting periodic orbit. Moreover, there is a set of parameters of positive measure for which chaos occurs.

"CONNECT-THE-DOTS" TREE MAPS

1995 ◽  
Vol 05 (05) ◽  
pp. 1427-1431
Author(s):  
LLUÍS ALSEDÀ ◽  
JOHN GUASCHI ◽  
JÉRÔME LOS ◽  
FRANCESC MAÑOSAS ◽  
PERE MUMBRÚ
Keyword(s):  
Piecewise Monotone ◽  
Interval Maps ◽  
Work In Progress ◽  
Monotone Map ◽  
The Given

We announce the main results of work in progress on piecewise monotone models for patterns of tree maps. More precisely, we define a notion of pattern for tree maps, and given such a pattern, we construct a tree and a piecewise monotone map on this tree with the same pattern. This piecewise monotone model has the least entropy among all models exhibiting the given pattern and has "minimal dynamics". We also give a formula to compute this minimal entropy directly from the pattern. These results generalize the known results for interval maps and the results from Li & Ye [1993].

scholarly journals Subspaces of interval maps related to the topological entropy

2019 ◽  
pp. 1 ◽  
Author(s):  
Xiaoxin Fan ◽  
Jian Li ◽  
Yini Yang ◽  
Zhongqiang Yang
Keyword(s):  
Topological Entropy ◽  
Interval Maps

scholarly journals Asymptotic expansion of smooth interval maps

Astérisque ◽  
2020 ◽  
Vol 416 ◽  
pp. 33-63
Author(s):  
Juan RIVERA-LETELIER
Keyword(s):  
Asymptotic Expansion ◽  
Interval Maps
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