scholarly journals Attractors for maps with fractional inverse

2005 ◽  
Vol 2005 (3) ◽  
pp. 343-355 ◽  
Author(s):  
M. R. Ferchichi ◽  
I. Djellit
Keyword(s):  
Two Dimensional ◽  
Focal Points ◽  
New Concepts ◽  
Specific Contact ◽  
Dynamical Properties ◽  
Dynamic Phenomena

In this work, we consider some dynamical properties and specific contact bifurcations of two-dimensional maps having an inverse with vanishing denominator. We introduce new concepts and notions of focal points and prefocal curves which may cause and generate new dynamic phenomena. We put in evidence a link existing between basin bifurcation of a map with fractional inverse and the prefocal curve of this inverse.

PLANE MAPS WITH DENOMINATOR I: SOME GENERIC PROPERTIES

1999 ◽  
Vol 09 (01) ◽  
pp. 119-153 ◽  
Author(s):  
GIAN-ITALO BISCHI ◽  
LAURA GARDINI ◽  
CHRISTIAN MIRA
Keyword(s):  
Invariant Sets ◽  
Two Dimensional ◽  
Focal Points ◽  
Generic Properties ◽  
New Concepts ◽  
Dynamical Properties ◽  
Basin Boundaries ◽  
Dynamic Phenomena

This paper is devoted to the study of some global dynamical properties and bifurcations of two-dimensional maps related to the presence, in the map or in one of its inverses, of a vanishing denominator. The new concepts of focal points and of prefocal curves are introduced in order to characterize some new kinds of contact bifurcations specific to maps with denominator. The occurrence of such bifurcations gives rise to new dynamic phenomena, and new structures of basin boundaries and invariant sets, whose presence can only be observed if a map (or some of its inverses) has a vanishing denominator.

scholarly journals On Some Properties of Focal Points

2009 ◽  
Vol 2009 ◽  
pp. 1-11
Author(s):  
M. R. Ferchichi ◽  
I. Djellit
Keyword(s):  
Fixed Point ◽  
Focal Point ◽  
Two Dimensional ◽  
Focal Points ◽  
Dynamical Properties

We consider some dynamical properties of two-dimensional maps having an inverse with vanishing denominator. We put in evidence a link between a fixed point of a map with fractional inverse and a focal point of this inverse.

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.

scholarly journals Dynamical properties of ring dark soliton in quasi-two dimensional Bose-Einstein condensates

2008 ◽  
Vol 57 (11) ◽  
pp. 6786
Author(s):  
Zhang Wei-Xi ◽  
Wang Deng-Long ◽  
Ding Jian-Wen
Keyword(s):  
Dark Soliton ◽  
Two Dimensional ◽  
Dynamical Properties ◽  
Bose Einstein

scholarly journals Ab-initio study of dynamical properties of two dimensional MoS2 under strain

AIP Advances ◽  
2015 ◽  
Vol 5 (10) ◽  
pp. 107103 ◽  
Author(s):  
Himadri Soni ◽  
Prafulla K. Jha
Keyword(s):  
Ab Initio ◽  
Two Dimensional ◽  
Ab Initio Study ◽  
Dynamical Properties

THE DYNAMICS AND STATISTICS OF BIVARIATE CHAOTIC MAPS IN COMMUNICATIONS MODELING

2004 ◽  
Vol 14 (04) ◽  
pp. 1177-1194 ◽  
Author(s):  
RACHEL M. HILLIAM ◽  
ANTHONY J. LAWRANCE
Keyword(s):  
Chaotic Maps ◽  
Two Dimensional ◽  
Arnold Cat Map ◽  
Chebyshev Map ◽  
Shift Keying ◽  
Dynamical Properties ◽  
Chaos Shift Keying

Statistical and dynamical properties of bivariate (two-dimensional) maps are less understood than their univariate counterparts. This paper gives a synthesis of extended results with exemplifications by bivariate logistic maps, the bivariate Arnold cat map and a bivariate Chebyshev map. The use of synchronization from bivariate maps in communication modeling is exemplified by an embryonic chaos shift keying system.

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