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#### djbinder

##### Guest

djbinder Asks:

If I have an autonomous series of differential equations $$\tag{1} \frac{dx_i}{dt} ~=~ A_i(x_1,...,x_n)$$ with the condition that $$\tag{2} \sum_{i=1}^n\frac{\partial A_i}{\partial x_i}~=~0$$ in all regions of phase space, can this be written as a Hamiltonian system in terms of some generalized position and momentum coordinates?

*When can an autonomous system be written using a Hamiltonian?*If I have an autonomous series of differential equations $$\tag{1} \frac{dx_i}{dt} ~=~ A_i(x_1,...,x_n)$$ with the condition that $$\tag{2} \sum_{i=1}^n\frac{\partial A_i}{\partial x_i}~=~0$$ in all regions of phase space, can this be written as a Hamiltonian system in terms of some generalized position and momentum coordinates?

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