# Tagged Questions

In dynamical systems, the motion of a particle in some geometric space, governed by some time dependent rules, is studied. The process can be discrete (where the particle jumps from point to point) or continuous (where the particle follows a trajectory). Dynamical systems is used in mathematical ...

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### Actual Classification re Nielsen-Thurston Theorem (how to)?

according to Nielsen -Thurston Classification: http://en.wikipedia.org/wiki/Nielsen%E2%80%93Thurston_classification If $S$ is compact and orientable surface, then any homeomorphism is isotopic to (...
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### Question about Chebyshev Polynomials in Beardon

I happen to be reading through Beardon's book, Iteration of Rational Functions, and I have come across a statement I don't quite believe. He uses it a little later on, so I'm concerned with clearing ...
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### Wronskian and roots

I am given an ODE $$-y''(x) + q(x) y(x) = \lambda y(x),$$ and let $y_1,y_2$ be two solutions to this ODE on $[a,b]$ to two different values $\lambda_1 \neq \lambda_2$(on the right side of this ...
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### Linear dynamical systems

Show that, if the real system $$\dot{x}=\left(\begin{array}{cc}\alpha&-\beta\\\beta&\alpha\end{array}\right)x$$ is diagonalised over the complex numbers $\mathbb{C}$, such that the ...
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