# Tagged Questions

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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### Can tearing a piece of paper be chaotic?

When one thinks of chaos, then automatically the thought pops up that a very little difference in the initial conditions enlarges over time and you end up with a totally different end situation. When ...
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### Initial conditions for a non-chaotic double pendulum

I know that the initial condition of the full double pendulum being horizontal yields motion that is not chaotic. Is there another set of initial conditions that would yield non-chaotic motion? Or do ...
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### Can quantum fluctuations affect the double pendulum?

The double pendulum is a simple example of a chaotic system which is extremely sensitive to tiny perturbations in its initial conditions. If we set off two identical double pendulum systems from ...
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### Does Lyapunov exponent equate to exponential inflation?

Physics can be modeled by dynamical systems $f^t(x)$ as well as by PDEs. The most common dynamical system has hyperbolic fixed point and can be an attractor or a repellor. The dynamics at repellors ...
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### What is a stroboscopic map?

I have an assignment where I'm supposed to generate a "stroboscopic map" of some orbits of a dynamical system. I have a hard time finding information about exactly what this kind of map is on the ...
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### Origin of chaos in Chua's circuit

I am doing a project on Chua's circuit, but I can't seem to find anything that explains where the chaotic nature of the system comes from. Does anyone know of articles that explain it well on an ...
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### Change of variables to apply Melnikov method

Supposing there is a system of non-autonomous non-linear differential equations with small damping and small forcing. The unperturbed system (zero damping and forcing) is Hamiltonian but neither has a ...
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### Hysteresis in the Lorenz Equations

I was going through Strogatz's wonderful book on nonlinear dynamics and while reading through one problem he posed at the end of the chapter, I did not really understand what was going on. So I hope ...
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### What are resonant tori?

What is the definition of a resonant/invariant torus (in the phase space of a Hamiltonian system)? Are there non-resonant tori?
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### Dynamical localisation in delta-kicked rotor

The quantum delta-kicked rotor is a common tool for studying quantum chaos. The energy of the rotor increases ballistically when kicking at the Talbot time (resonance) and jumps between zero and some ...
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### Logistic map and attractors

Does the logistic map have a strange attractor for some "chaotic" values of the parameter?
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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 ...
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### T-Symmetry and spatial symmetry of a multivariate conserved quantity

Definition: A reversible system is defined to be any second-order system that is invariant under the map. $t \mapsto -t$ $y \mapsto -y$ Suppose there exists a multivariate function \$f(x,...
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### What is the temperature evolution of the conductance of a quantum chaotic system?

I read this really nice article by Abanin and Levitov: http://arxiv.org/pdf/0704.3608.pdf They argued that the mixing of the quantum edge channel at the vicinity of a PN junction is described by the ...