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From attractor to chaotic saddle: a tale of transverse instability
Suppose that a dynamical system possesses an invariant submanifold, and the restriction of the system to this submanifold has a chaotic attractor A. Under which conditions is A an attractor for theExpand
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Bubbling of attractors and synchronisation of chaotic oscillators
We present a system of two coupled identical chaotic electronic circuits that exhibit a blowout bifurcation resulting in loss of stability of the synchronised state. We introduce the concept ofExpand
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Robust Simulations of Turing Machines with Analytic Maps and Flows
TLDR
In this paper, we show that closed-form analytic maps and flows can simulate Turing machines in an error-robust manner. Expand
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Liapunov stability and adding machines
In Chapter 1 we discussed several notions of stability for compact invariant sets of dynamical systems. Here we shall prove that, under very general hypotheses, the set of connected components of aExpand
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Computability with polynomial differential equations
TLDR
In this paper, we show that there are initial value problems defined with polynomial ordinary differential equations that can simulate universal Turing machines in the presence of bounded noise. Expand
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Exotic Attractors: From Liapunov Stability to Riddled Basins
1 Attractors in Dynamical Systems.- 1.1 Introduction.- 1.2 Basic definitions.- 1.3 Topological and dynamical consequences.- 1.4 Attractors.- 1.5 Examples and counterexamples.- 1.6 Historical remarksExpand
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Symmetry-breaking as an origin of species
A central problem in evolutionary biology is the occurrence in the fossil record of new species of organisms. Darwin's view, in The Origin of Species, was that speciation is the result of gradualExpand
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On differentiability and analyticity of positive definite functions
We derive a set of differential inequalities for positive definite functions based on previous results derived for positive definite kernels by purely algebraic methods. Our main results show thatExpand
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Eigenvalues of Positive Definite Integral Operators on Unbounded Intervals
Let k(x, y) be the positive definite kernel of an integral operator on an unbounded interval of ℝ. If k belongs to class defined below, the corresponding operator is compact and trace class. WeExpand
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Local stationarity of L2(ℝ) processes
TLDR
This paper shows how the sampling theorem relates with the variations along time of the second order statistics of L2(ℝ) nonstationary processes. Expand
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