منابع مشابه
Torus breakdown in noninvertible maps.
We propose a criterion for the destruction of a two-dimensional torus through the formation of an infinite set of cusp points on the closed invariant curves defining the resonance torus. This mechanism is specific to noninvertible maps. The cusp points arise when the tangent to the torus at the point of intersection with the critical curve L(0) coincides with the eigendirection corresponding to...
متن کاملHomoclinic tangles for noninvertible maps
Not all naturally occurring iterated systems have the property that time is reversible. In which case, the dynamics must be modelled by a noninvertible map rather than by a di eomorphism. While one-dimensional theory describes dynamics of noninvertible maps, higher-dimensional theory has focussed on di eomorphisms, though there are many higher-dimensional examples of natural systems modelled by...
متن کاملGeneralized synchronization of chaos in noninvertible maps.
The properties of functional relation between a noninvertible chaotic drive and a response map in the regime of generalized synchronization of chaos are studied. It is shown that despite a very fuzzy image of the relation between the current states of the maps, the functional relation becomes apparent when a sufficient interval of driving trajectory is taken into account. This paper develops a ...
متن کاملSlow-fast Dynamics Generated by Noninvertible Plane Maps
The present paper focuses on the two time scale dynamics generated by 2D polynomial noninvertible maps T of (Z0−Z2) and (Z1−Z3−Z1) types. This symbolism, specific to noninvertible maps, means that the phase plane is partitioned into zones Zk, where each point possesses the k real rank-one preimages. Of special interest here is the structure of slow and fast motion sets of such maps. The formati...
متن کاملPlane Maps with denominator. Part II: Noninvertible Maps with Simple Focal Points
This paper is the second part of an earlier work devoted to the properties specific to maps of the plane characterized by the presence of a vanishing denominator, which gives rise to the generation of new types of singularities, called set of nondefinition, focal points and prefocal curves. A prefocal curve is a set of points which are mapped (or “focalized”) into a single point, called focal p...
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ژورنال
عنوان ژورنال: Scholarpedia
سال: 2007
ISSN: 1941-6016
DOI: 10.4249/scholarpedia.2328