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In university I have learnt about the concept of tensors, which are multilinear maps in that it is a map such that it is linear with respect to all its arguments

$$f(a+b+c+d+e+f+g....)=f(a)+f(b)+...+f(g)+...$$

and in physics, it is geometric in that it is independent of basis

In biophysics I learn about the Phenomenological equations which tells how vectorial and scalar flows are related to each other by some coefficients

$$L_{11}V+L_{12}S=V$$ $$L_{21}S+L_{22}S=S$$

which when turbulence are present, the "Lij"s will be higher order (n>1) tensors

Also in general relativity, tensors are commonly used objects in modelling the dynamics of spacetime

Given how the examples I list (possibly more) involve modelling nonlinear phenomenon with tensors and other multilnear maps

Are there systems so nonlinear that even multilinear systems cannot be used to model them and they must be analysed as it is?. If so what are the famous examples so that I can read more about them?

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