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Iterated maps on the interval as dynamical systems

- P. Collet, J. Eckmann
- Mathematics
- 1980

Motivation and Interpretation.- One-Parameter Families of Maps.- Typical Behavior for One Map.- Parameter Dependence.- Systematics of the Stable Periods.- On the Relative Frequency of Periodic and… Expand

A global attracting set for the Kuramoto-Sivashinsky equation

- P. Collet, J. Eckmann, H. Epstein, J. Stubbe
- Mathematics
- 1 February 1993

AbstractNew bounds are given for the L2-norm of the solution of the Kuramoto-Sivashinsky equation
$$\partial _t U(x,t) = - (\partial _x^2 + \partial _x^4 )U(x,t) - U(x,t)\partial _x U(x,t)$$
, for… Expand

Statistics of closest return for some non-uniformly hyperbolic systems

- P. Collet
- MathematicsErgodic Theory and Dynamical Systems
- 23 April 1999

For non-uniformly hyperbolic maps of the interval with exponential decay of correlations we prove that the law of closest return to a given point when suitably normalized is almost surely… Expand

Quasi-stationary distributions and diffusion models in population dynamics

- P. Cattiaux, P. Collet, A. Lambert, S. Martínez, S. M'el'eard, Jaime San Martín
- Mathematics
- 27 March 2007

In this paper, we study quasi-stationarity for a large class of Kolmogorov diffusions. The main novelty here is that we allow the drift to go to $- \infty$ at the origin, and the diffusion to have an… Expand

Quasi-Stationary Distributions: Markov Chains, Diffusions and Dynamical Systems

- P. Collet, S. Martínez, Jaime San Martín
- Mathematics
- 25 October 2012

1.Introduction.- 2.Quasi-stationary Distributions: General Results.- 3.Markov Chains on Finite Spaces.- 4.Markov Chains on Countable Spaces.- 5.Birth and Death Chains.- 6.Regular Diffusions on [0,… Expand

Analyticity for the Kuramoto-Sivashinsky equation

- P. Collet, J. Eckmann, H. Epstein, J. Stubbe
- Mathematics
- 1 September 1993

Abstract We study the analyticity properties of solutions of the Kuramoto-Sivashinsky equation ∂tU (x,t) = -(∂2x + ∂4x) U(x, t) − U(x, t) ∂xU (x,t), for initial data which are periodic with period L.… Expand

Universal properties of maps on an interval

- P. Collet, J. Eckmann, O. Lanford
- Mathematics
- 1 September 1980

We consider itcrates of maps of an interval to itself and their stable periodic orbits. When these maps depend on a parameter, one can observe period doubling bifurcations as the parameter is varied.… Expand

Concentration inequalities for random fields via coupling

- J. Chazottes, P. Collet, C. Külske, F. Redig
- Mathematics, Physics
- 23 March 2005

We present a new and simple approach to concentration inequalities in the context of dependent random processes and random fields. Our method is based on coupling and does not use information… Expand

A rigorous model study of the adaptive dynamics of Mendelian diploids

- P. Collet, S. Méléard, J. Metz
- Mathematics, BiologyJournal of mathematical biology
- 27 November 2011

TLDR

An optimisation method for separating and rebuilding one-dimensional dispersive waves from multi-point measurements. Application to elastic or viscoelastic bars

When using a classical SHPB (split Hopkinson pressure bar) set-up, the useful measuring time is limited by the length of the bars, so that the maximum strain which can be measured in material testing… Expand

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