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Hybrid matrix models and their population dynamic consequences

Sanyi Tang (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, the main purpose is to reveal what kind of qualitative dynamical changes a continuous age-structured model may undergo as continuous reproduction is replaced with an annual birth pulse. Using the discrete dynamical system determined by the stroboscopic map we obtain an exact periodic solution of system with density-dependent fertility and obtain the threshold conditions for its stability. We also present formal proofs of the supercritical flip bifurcation at the bifurcation as...

Hyperbolic components of the complex exponential family

Robert L. Devaney, Nuria Fagella, Xavier Jarque (2002)

Fundamenta Mathematicae

We describe the structure of the hyperbolic components of the parameter plane of the complex exponential family, as started in [1]. More precisely, we label each component with a parameter plane kneading sequence, and we prove the existence of a hyperbolic component for any given such sequence. We also compare these sequences with the more commonly used dynamical kneading sequences.

Hyperbolic homeomorphisms and bishadowing

P. E. Kloeden, J. Ombach (1997)

Annales Polonici Mathematici

Hyperbolic homeomorphisms on compact manifolds are shown to have both inverse shadowing and bishadowing properties with respect to a class of δ-methods which are represented by continuous mappings from the manifold into the space of bi-infinite sequences in the manifold with the product topology. Topologically stable homeomorphisms and expanding mappings are also considered.

Hyperbolic measure of maximal entropy for generic rational maps of ℙ k

Gabriel Vigny (2014)

Annales de l’institut Fourier

Let f be a dominant rational map of ℙ k such that there exists s < k with λ s ( f ) > λ l ( f ) for all l . Under mild hypotheses, we show that, for A outside a pluripolar set of Aut ( ℙ k ) , the map f ∘ A admits a hyperbolic measure of maximal entropy log λ s ( f ) with explicit bounds on the Lyapunov exponents. In particular, the result is true for polynomial maps hence for the homogeneous extension of f to ℙ k + 1 . This provides many examples where non uniform hyperbolic dynamics is established.One of the key tools is to approximate the graph of a meromorphic...

Hyperbolic systems on nilpotent covers

Yves Coudene (2003)

Bulletin de la Société Mathématique de France

We study the ergodicity of the weak and strong stable foliations of hyperbolic systems on nilpotent covers. Subshifts of finite type and geodesic flows on negatively curved manifolds are also considered.

Hyperbolicity in a class of one-dimensional maps.

Gregory J. Davis (1990)

Publicacions Matemàtiques

In this paper we provide a direct proof of hyperbolicity for a class of one-dimensional maps on the unit interval. The maps studied are degenerate forms of the standard quadratic map on the interval. These maps are important in understanding the Newhouse theory of infinitely many sinks due to homoclinic tangencies in two dimensions.

Hyper-dependence, hyper-ageing properties and analogies between them: a semigroup-based approach

Rachele Foschi (2013)

Kybernetika

In previous papers, evolution of dependence and ageing, for vectors of non-negative random variables, have been separately considered. Some analogies between the two evolutions emerge however in those studies. In the present paper, we propose a unified approach, based on semigroup arguments, explaining the origin of such analogies and relations among properties of stochastic dependence and ageing.

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