# Questions tagged [nonlinear-analysis]

For questions on nonlinear analysis, a branch of mathematical analysis that deals with nonlinear mappings.

225 questions
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### Nonlinear transformation of region from $\mathbb R^2\to\mathbb R^2$

If I have a given continuous nonlinear map $T:\mathbb{R}^2\rightarrow \mathbb{R}^2$, and a region $D \subset \mathbb{R}^2$, is it necessarily true that $T(\partial D)=\partial T(D)$? That is, do ...
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### Integration of first order second degree partial differential equation [on hold]

How to evaluate it's integral? $$\int \left( \frac{dp}{dx} \right)^2 \, dx$$
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### Is there such branch as Nonlinear Matrix Algebra?

Is there such branch as nonlinear matrix algebra, that researches nonlinear functions with matrix (tensor) valued arguments and outputs where nonlinearities are applied componentwise. Such functions ...
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### What algorithm to use to find the non-linear mapping function between 2D shapes generated from biosignals attractors?

I have two biosignals recording the same phenomenon with different methods. Target signal is a reference signal and I would like to find some non-linear mapping from the original signal to the ...
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### To show that a 2D nonlinear ODE undergoes a pitchfork bifurcation

Show that a pitchfork bifurcation occurs when $\mu = 0$ for the system $$\dot{x} = \mu x + xy + 3y^2$$ $$\dot{y} = -2y + x^2 + 2xy^2$$. Attempt at a solution If $\dot{x} = 0$ then x = \frac{-3y}{\...
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### To show that $\dot{x} = -y - x +y^2 - x^2,\; \dot{y} = xy$ has no periodic orbits.

I've tried using index theory, but there's a non-isolated fixed point at $(0, 0)$ (the remaining fixed points at $(0, 1)$ and $(-1, 0)$ are saddles). The terms in the equations have even indices and ...
### Proof check: Show that $x_{n + 1} = f(x_n) = 15 - x_n^2$ is a (Smale) horseshoe
A solution is given here: However, I believe it to be incorrect because $f(K_1) = f(K_2) \neq (-\sqrt{15}, \sqrt{15})$. Attempt at a solution: Referring to the diagram from the question... By the ...
I am trying to construct some examples of the nonexpansive mapping $T$ from $R^2$ to $R^2$ such that $T$ should have fixed points more than one. But I could not construct. Can somebody help me? Please....