# Tagged Questions

For questions in chaos theory.

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### Can combinatorics with chaos theory help find winners in horse racing? [closed]

Can combinatorics with chaos theory help find winners in horse racing? In horse racing there is a random pattern that will show up when playing long enough.
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### Infinite tetration of $-2.5$

Let $a_n$ be the sequence $z, z^z, z^{z^z} ...$ for $z \in \mathbb{C}$. This is sometimes called the iterated exponential with base $z$. I am investigating the above sequence for $z = -2.5$. After ...
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### Examples of transient chaos in the quasi-periodic route to chaos?

I have read that transient chaos has been observed experimentally where a quasiperiodic steady state is involved (e.g. in Ytrium Crystals). I have also read about examples of equations which show ...
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### What methods can I use to model a seemingly chaotic set of values? [closed]

If I have a graph/set of data, what methods can I use to model the data to predict a likely next set of values? For example, given the following numbers [ 2, 4, 5, 2, 1, -1, -2, 0 ], are there some ...
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### Finding a parametrization of the solutions of $\frac{dx}{dt}=\frac{\sinh y}{\cosh y+A\cos x}$, $\frac{dy}{dt}=\frac{A\sin x}{\cosh y+A\cos x}$

I am trying desperately to find a parametrization for the following: $\frac{dx}{dt}=\frac{\sinh y}{\cosh y+A\cos x}$ $\frac{dy}{dt}=\frac{A\sin x}{\cosh y+A\cos x}$ I tried to devide the equation ...
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### Permutations in an Infinite List of Random Numbers

In an infinite list of random numbers from a to b, prove that in this list, there are all possible permutations of n numbers from the list, where n can be any number. Here are some versions of the ...
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### generating functions for catastrophe theory

I am studying Thom's theorem in catastrophe theory and am having a hard time understanding what the "generating functions" actually do. How exactly are they used to classify generic caustics? The ...
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### How to know whether a solution for a set of coupled non-linear differential equations are stable or not

I have 3-coupled ordinary non-linear differential equations, one second order in time and other two first order in time, with 3-dependant variables say x(t), y(t) and z(t). I have a particular ...
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### Is Fractal Dimension Really Enough to Diagnose Chaos?

I've been reading a fair amount about the relationship between fractality and chaos. While approximating the dominant Lyapunov exponent seems to be the preferred method for diagnosing chaos, it seems ...
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### What is the difference between high dimensional and low dimensional chaos?

Often I read of high and low dimensional chaos. But, I don't know what is their difference. I have thought the following answer. Let us consider a time series $\{x_i\}_{i\in\mathbb N}$. According to ...
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### What is computational complexity of a coding technique

In my previous Question Help in understanding a coding technique based on inverse mapping of a dynamical system I learnt how to apply chaotic map in coding theory in communications. Steps: (1) The ...
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### Very different starting conditions into similar outcomes within Chaos Theory.

Chaos Theory demonstrates how systems with very similar starting conditions can end up in very different states, but can it demonstrate whether systems with very different starting conditions can end ...