Chaos theory is the study of systems that are highly sensitive to slight, even imperceptible changes in initial conditions. This is popularly known as the butterfly effect. Many natural systems exhibit chaotic behavior, including weather and electron orbitals.

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Does the logistic map have an attractor for a particular value of the parameter?

Background: Currently I am studying a course on non-linear dynamics. We have been studying about attractors only intuitively, so I do not have a definition for an attractor. Let me give you a couple ...
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Is there a one-to-one mapping between numeric sequences and symbolic representations?

I am not a physicist but applying symbolic dynamics for information coding in signal processing. I have represented a chaotic signal obtained from Lorenz system into {0,1}. Then this symbolic sequence ...
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meaning of Smooth Dynamical System?

What does smooth dynamical system mean? It is the title of a paper I am supposed to read in non linear systems.
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What is the event in history where iterated functions became appropriate for modeling physics?

Wolfram as well as Aldrovandi and Freitas 1 maintain that iterated functions $f^t(x)$ are a valid alternative to PDEs for modelling physics. Instead of just citing 1, I want to be able to cite the ...
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Reference for the Landau-Lifshitz system

I'm interested in understanding the dynamics of the discrete Landau-Lifshitz system. It's solutions to equations like $$\frac{\partial X_n}{\partial t} = X_n\times (X_{n-1}+X_{n+1})$$ where the $X_n$ ...
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Kolmogorov entropy and noise

There are various ways of calculating the Kolmogorov entropy (KE)of dynamical system. According to Pesin's theorum, it is the summation of the lyapunov exponents; frominformation theoretic concet, it ...
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The ideal trampoline

Suppose we have a mass attached to the top of an ideal (linear and massless) spring oriented vertically in a uniform gravitational field, and on top of that mass there is another mass resting on it. ...
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spectral eigenvalue staircase and quantum system

in a d-dimensional system of Quantum physics , does the Eigenvalue staircase $ N(E)= \sum_{E_{n}\le E} 1 $ determine ALL the properties of Quantum System ?? for example, let us assume that the ...