ABOUT A NEW CLASS OF INVARIANT AREAS GENERATED BY TWO-DIMENSIONAL ENDOMORPHISMS

2003 ◽  
Vol 13 (04) ◽  
pp. 905-933 ◽  
Author(s):  
J. C. CATHALA
Keyword(s):  
Mixed Type ◽  
Two Dimensional ◽  
New Class ◽  
Attracting Set ◽  
Critical Curves

Invariant areas generated by two-dimensional endomorphisms are studied using the method of critical curves. The invariant areas considered in this paper are obtained by iterating the noninvariant set constituted by the connected basin of an attracting set or the immediate basin of a nonconnected basin. This new kind of invariant area is of mixed type in the sense that its boundary is made up of critical curves arcs and arcs of saddle manifolds. The presentation is illustrated by three examples. A bifurcation changing the degree of connexity of an invariant area is described.

FRACTAL AGGREGATION OF BASIN ISLANDS IN TWO-DIMENSIONAL QUADRATIC NONINVERTIBLE MAPS

1995 ◽  
Vol 05 (04) ◽  
pp. 991-1019 ◽  
Author(s):  
C. MIRA ◽  
C. RAUZY
Keyword(s):  
Phase Plane ◽  
Parameter Variation ◽  
The Other ◽  
Two Dimensional ◽  
Quadratic Maps ◽  
Attracting Set ◽  
Critical Curves ◽  
Noninvertible Maps

Properties of basins of noninvertible maps of the plane are studied by using the method of critical curves. The paper considers the simplest class of quadratic maps, that having a phase plane made up of two regions, one with two first rank preimages, the other with no preimage, in situations different from those described in a previous publication. More specifically, the considered quadratic maps give rise to a basin made up of infinitely many nonconnected regions, a parameter variation leading to an aggregation of these regions, which occur in a fractal way. The nonconnected regions, different from that containing an attracting set, are called "islands".

New Methods for Analyzing Water Pollutants

1982 ◽  
Vol 14 (4-5) ◽  
pp. 59-71 ◽  
Author(s):  
L H Keith ◽  
R C Hall ◽  
R C Hanisch ◽  
R G Landolt ◽  
J E Henderson
Keyword(s):  
Amino Acids ◽  
Gas Chromatography ◽  
Two Dimensional ◽  
Gas Chromatograph ◽  
New Class ◽  
New Methods ◽  
System A ◽  
Drinking Waters ◽  
Computer Controlled ◽  
Nitrogen Containing Compounds

Two new methods have been developed to analyze for organic pollutants in water. The first, two-dimensional gas chromatography, using post detector peak recycling (PDPR), involves the use of a computer-controlled gas Chromatograph to selectively trap compounds of interest and rechromatograph them on a second column, recycling them through the same detector again. The second employs a new detector system, a thermally modulated electron capture detector (TMECD). Both methods were used to demonstrate their utility by applying them to the analysis of a new class of potentially ubiquitous anthropoaqueous pollutants in drinking waters- -haloacetonitriles. These newly identified compounds are produced from certain amino acids and other nitrogen-containing compounds reacting with chlorine during the disinfection stage of treatment.

scholarly journals Covalent assembly of a two-dimensional molecular “sponge” on a Cu(111) surface: confined electronic surface states in open and closed pores

2014 ◽  
Vol 50 (57) ◽  
pp. 7628-7631 ◽  
Author(s):  
Aneliia Shchyrba ◽  
Susanne C. Martens ◽  
Christian Wäckerlin ◽  
Manfred Matena ◽  
Toni Ivas ◽  
...  
Keyword(s):  
Surface States ◽  
Two Dimensional ◽  
New Class ◽  
Trimesic Acid ◽  
Electronic Surface

We present a new class of on-surface covalent reactions, formed between diborylene-3,4,9,10-tetraaminoperylene and trimesic acid on Cu(111), which gives rise to a porous 2D-‘sponge’.

KNOT POINTS IN TWO-DIMENSIONAL MAPS AND RELATED PROPERTIES

2009 ◽  
Vol 19 (02) ◽  
pp. 545-555 ◽  
Author(s):  
F. TRAMONTANA ◽  
L. GARDINI ◽  
D. FOURNIER-PRUNARET ◽  
P. CHARGE
Keyword(s):  
Focal Point ◽  
Singular Line ◽  
Two Dimensional ◽  
Focal Points ◽  
Singular Set ◽  
One Dimensional ◽  
Attracting Set ◽  
Straight Line ◽  
Special Character ◽  
Stable And Unstable Sets

We consider the class of two-dimensional maps of the plane for which there exists a whole one-dimensional singular set (for example, a straight line) that is mapped into one point, called a "knot point" of the map. The special character of this kind of point has been already observed in maps of this class with at least one of the inverses having a vanishing denominator. In that framework, a knot is the so-called focal point of the inverse map (it is the same point). In this paper, we show that knots may also exist in other families of maps, not related to an inverse having values going to infinity. Some particular properties related to focal points persist, such as the existence of a "point to slope" correspondence between the points of the singular line and the slopes in the knot, lobes issuing from the knot point and loops in infinitely many points of an attracting set or in invariant stable and unstable sets.

BASIN BIFURCATIONS OF TWO-DIMENSIONAL NONINVERTIBLE MAPS: FRACTALIZATION OF BASINS

1994 ◽  
Vol 04 (02) ◽  
pp. 343-381 ◽  
Author(s):  
C. MIRA ◽  
D. FOURNIER-PRUNARET ◽  
L. GARDINI ◽  
H. KAWAKAMI ◽  
J.C. CATHALA
Keyword(s):  
Phase Plane ◽  
The Other ◽  
Two Dimensional ◽  
Basin Boundary ◽  
Critical Curves ◽  
Noninvertible Maps

Properties of the basins of noninvertible maps of a plane are studied using the method of critical curves. Different kinds of basin bifurcation, some of them leading to basin boundary fractalization are described. More particularly the paper considers the simplest class of maps that of a phase plane which is made up of two regions, one with two preimages, the other with no preimage.

The half-plane diffraction problem for harmonic time dependence

1959 ◽  
Vol 252 (1270) ◽  
pp. 411-417 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Time Dependence ◽  
Boundary Value Problems ◽  
Half Plane ◽  
Mixed Type ◽  
Boundary Value ◽  
Diffraction Problem ◽  
Two Dimensional ◽  
Conducting Screen ◽  
Plane Diffraction

Green’s functions are obtained for the boundary-value problems of mixed type describing the general two-dimensional diffraction problems at a screen in the form of a half-plane (Sommerfeld’s problem), applicable to acoustically rigid or soft screens, and to the full electromagnetic field at a perfectly conducting screen.

scholarly journals Copper halide diselenium: predicted two-dimensional materials with ultrahigh anisotropic carrier mobilities

RSC Advances ◽  
2020 ◽  
Vol 10 (14) ◽  
pp. 8016-8026 ◽  
Author(s):  
Fazel Shojaei ◽  
Maryam Azizi ◽  
Zabiollah Mahdavifar ◽  
Busheng Wang ◽  
Gilles Frapper
Keyword(s):  
Band Gap ◽  
First Principles ◽  
Two Dimensional ◽  
Copper Halide ◽  
New Class ◽  
Two Dimensional Materials ◽  
Bonding Properties ◽  
High Carrier ◽  
Indirect Band Gap ◽  
Very High

The physical and bonding properties of a new class of two-dimensional materials – CuXSe2 (X = Cl, Br) – are investigated using first-principles methods. 2D CuXSe2 are indirect band gap and possess extremely anisotropic and very high carrier mobilities.

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