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Iterated maps on the interval as dynamical systems
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
A global attracting set for the Kuramoto-Sivashinsky equation
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
Statistics of closest return for some non-uniformly hyperbolic systems
  • P. Collet
  • Mathematics
    Ergodic 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
Quasi-stationary distributions and diffusion models in population dynamics
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
Quasi-Stationary Distributions: Markov Chains, Diffusions and Dynamical Systems
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,
Analyticity for the Kuramoto-Sivashinsky equation
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.
Universal properties of maps on an interval
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.
Concentration inequalities for random fields via coupling
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
A rigorous model study of the adaptive dynamics of Mendelian diploids
TLDR
It is proved under the usual smoothness assumptions, starting from a stochastic birth and death process model, that, when advantageous mutations are rare and mutational steps are not too large, the population behaves on the mutational time scale as a jump process moving between homozygous states (the trait substitution sequence of the adaptive dynamics literature).
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
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