# Questions tagged [chaos-theory]

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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### Assumptions in the bound on chaos

In the paper A bound on chaos, by Maldacena, Shenker and Stanford. They mention two assumptions to prove that the Lyapunov exponent in the OTOCs must be smaller than or equal to $2\pi T$. One of the ...
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1 vote
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### Is a free rigid body in 3D space an integrable system? [duplicate]

I am trying to find three integrable systems with 6 degrees of freedom using the Liouville–Arnold theorem. That means that a set of integrals of motion that correspond to a conserved quantity for ...
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### Why Black Hole is maximally chaotic?

I understand intuitively that black holes are chaotic. However, people say black holes are not just chaotic, they are "maximally chaotic". What is the quantitative definition of "...
1 vote
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### Stroboscopic map

I am trying to plot the stroboscopic map of the classical kicked rotor, which is characterized by the equations: $$p_{n+1} = p_n - \frac{dV}{dx}|_{x=x_n}$$ $$x_{n+1} = x_n +p_{n+1}$$ where $x_n$ is on ...
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### Why there’s level repulsion in quantum chaotic systems?

What’s the physical intuition of level repulsion in thermalized quantum systems? And from the opposite, why integratable systems display a Poisson distribution of the spectrum?
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### Does the value of Maximum Lyapunov exponent depend on the eigenvalues of the system?

I am currently reading this paper where on page 8, the authors say that: Negative eigenvalues correspond to unstable systems. This correlates with Figure 8 on page 12. Does it mean that there is a ...
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### Why the 3d Lorenz attractor has a butterfly shape? Why isn't it 3 dimensional too? [closed]

The Lorenz attractor has a butterfly shaped a strange attractor, but we plot it in 3D. Why is not it has a 3D shape too? It has a strange shape? It is a non-integer dimensional attractor.
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### Is it possible to realize a probabilistic Maxwell's demon using Tesla valve?

Imagine a container, with balls of diameter 1x and 10x, moving randomly in all directions. These balls are mixed, so it is a low order system. Now this container is connected to another container via ...
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### Do all dynamical systems have attractors?

Do all dynamical systems have attractors? Is there any chance that there are two or more absolutely the same sets of states in one attractor?
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### Distinguishing between chaos and multiperiodic oscillations from the Fourier spectrum

Consider a system which exhibits multiperiodicity, say with oscillations of the form $x(t) = \sum_{n=0} c_n \cos(n \omega_0 t)$, $\lim_{n \to \infty} c_n = 0$. The Fourier transform $\tilde{x}(\omega)$...
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### Per Newtonian mechanics, a coin toss exhibits deterministic chaos theory, but could relativity cause a probabilistic outcome of a coin toss?

It took me a long time to accept that a coin toss boils down to deterministic chaos theory. For example, the typical near 50/50 odds for outcomes of heads or tails results from complex initial ...
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### Boltzmann's equation for interacting case

Gravitation Foundations and Frontiers book by T. Padmanabhan tells in its first chapter that This result allows us to introduce distribution functions in relativistic theory in exact analogy with non-...
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### Lyapunov exponent of "real life"

Today I simply forgot watching soccer WM on TV, and promptly my national team lost. Assume there is a meaningful alternative universe where I turned on the TV (quantum and relativity theorists already ...
1 vote
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### Can a saddle point corresponding to black hole horizon act as a source of chaos?

I was going through this paper where on page 5 they argue that in the given Poincare section: Most of the orbits form regular tori, while we can also see that some tori near the saddle point of the ...
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### Literature reference: example of stable and unstable manifolds in Henon-Heiles system

There is a quite classical description of chaotic systems based on the behaviour of stable and unstable manifolds around a stationary point of the Poincaré section. It is presented, for example, [here,...
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