Journal ArticleDOI
Some properties of piecewise linear expanding maps
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This article is published in Nonlinear Analysis-theory Methods & Applications.The article was published on 1980-01-02. It has received 13 citations till now. The article focuses on the topics: Piecewise linear manifold & Piecewise.read more
Citations
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Journal ArticleDOI
Nonlinear modelling of cancer: Bridging the gap between cells and tumours
John Lowengrub,Hermann B. Frieboes,Hermann B. Frieboes,Fang Jin,Fang Jin,Yao-Li Chuang,Xiangrong Li,Paul Macklin,Steven M. Wise,Vittorio Cristini +9 more
TL;DR: In this paper, the authors provide an overview of multiscale modelling focusing on the growth phase of tumours and bypassing the initial stage of tumourigenesis, and limit the scope further by considering models of tumor progression that do not distinguish tumour cells by their age and do not consider immune system interactions nor do they describe models of therapy.
Book ChapterDOI
Topological Dynamics on the Interval
TL;DR: A great deal has been written about maps of the interval, especially in recent years as mentioned in this paper, and there have been a number of numerical studies and descriptive works (Co, Fe, GM, HoH, Ma2, MeS, Mr).
Journal ArticleDOI
On a class of transformations which have unique absolutely continuous invariant measures
Abraham Boyarsky,Manny Scarowsky +1 more
TL;DR: In this article, a class of piecewise C2 transformations from an interval into itself with slopes greater than 1 in absolute value, and having the property that it takes partition points into partition points is shown to have unique absolutely continuous invariant measures.
Journal ArticleDOI
Randomness implies order
TL;DR: In this paper, a density function p such that ∥ p − f ∗ ∥ and p is the invariant density of the stochastic difference equation xn + 1 = τ(xn) + W, where W is a random variable is presented.
Journal ArticleDOI
Quasi-invariant manifolds, stability, and generalized Hopf bifurcation
TL;DR: In this article, analisi completa del problema della biforcazione di Hopf relativa ad arbitrarie piccole perturbazioni del secondo membro di un'equazione differenziale in Rn, p=f0(p), soddisfano una condizione di non risonanza.
References
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Book ChapterDOI
Period Three Implies Chaos
TL;DR: In this article, a generalized logistic equation was used to model the distribution of points of impact on a spinning bit for oil well drilling, as mentioned if this distribution is helpful in predicting uneven wear of the bit.
Journal ArticleDOI
The dynamics of density dependent population models.
TL;DR: A theoretical analysis of the mathematical mechanisms underlying this complexity from the viewpoint of modern dynamical systems theory on a density-dependent Leslie model with two age classes and the existence of a "strange attractor" is demonstrated.
Journal ArticleDOI
Periodic points and chaotic functions in the unit interval
G.J. Butler,G. Pianigiani +1 more
TL;DR: In this paper, it was shown that the set of chaotic self-maps of the unit interval contains an open dense subset of the space of all continuous self-mappings of a unit interval.
Journal ArticleDOI
Chaotic difference equations are dense
TL;DR: In this paper, a continuous function mapping a compact interval of the real line into itself is called chaotic if the difference equation defined in terms of it behaves chaotically in the sense of Li and Yorke, and the set of all such chaotic functions is shown to toe a dense subset of the space of continuous mappings of that interval into itself with the max norm.