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Hybrid matrix models and their population dynamic consequences

Sanyi Tang (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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 well...

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 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 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.

Identifying points of a pseudo-Anosov homeomorphism

Gavin Band (2003)

Fundamenta Mathematicae

We investigate the question, due to S. Smale, of whether a hyperbolic automorphism T of the n-dimensional torus can have a compact invariant subset homeomorphic to a compact manifold of positive dimension, other than a finite union of subtori. In the simplest case such a manifold would be a closed surface. A result of Fathi says that T can sometimes have an invariant subset which is a finite-to-one image of a closed surface under a continuous map which is locally injective except possibly at a finite...

Infinitesimal conjugacies and Weil-Petersson metric

Albert Fathi, L. Flaminio (1993)

Annales de l'institut Fourier

We study deformations of compact Riemannian manifolds of negative curvature. We give an equation for the infinitesimal conjugacy between geodesic flows. This in turn allows us to compute derivatives of intersection of metrics. As a consequence we obtain a proof of a theorem of Wolpert.

Invariant densities for C¹ maps

Anthony Quas (1996)

Studia Mathematica

We consider the set of C 1 expanding maps of the circle which have a unique absolutely continuous invariant probability measure whose density is unbounded, and show that this set is dense in the space of C 1 expanding maps with the C 1 topology. This is in contrast with results for C 2 or C 1 + ε maps, where the invariant densities can be shown to be continuous.

Invariant graphs of functions for the mean-type mappings

Janusz Matkowski (2012)

ESAIM: Proceedings

Let I be a real interval, J a subinterval of I, p ≥ 2 an integer number, and M1, ... , Mp : Ip → I the continuous means. We consider the problem of invariance of the graphs of functions ϕ : Jp−1 → I with respect to the mean-type mapping M = (M1, ... , Mp).Applying a result on the existence and uniqueness of an M -invariant mean [7], we prove that if the graph of a continuous function ϕ : Jp−1 → I ...

Invariant jets of a smooth dynamical system

Sophie Lemaire (2001)

Bulletin de la Société Mathématique de France

The local deformations of a submanifold under the effect of a smooth dynamical system are studied with the help of Oseledets’ multiplicative ergodic theorem. Equivalence classes of submanifolds, called jets, are introduced in order to describe these local deformations. They identify submanifolds having the same approximations up to some order at a given point. For every order k , a condition on the Lyapunov exponents of the dynamical system is established insuring the convergence of the k -jet of...

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