Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

If we have a $\phi: \mathbb{R} \times \mathbb{R}^n \times \mathbb{R} \to \mathbb{R}$, $\phi = \phi(t, \mathbf{q},\alpha)$ one-parameter group of infinitesimal transformation which is $\mathcal{C}^2$ with respect to $t$ and $\mathbf{q}$, is it sufficient to $\phi$ to be differentiable with respect to $\alpha$ to write $$\phi = \phi(t, \mathbf{q}, 0) + \alpha \frac{\partial \phi}{\partial \alpha}(t, \mathbf{q}, 0) + o(\alpha)$$ if we want $\eta (t, \mathbf{q}) = \frac{\partial \phi}{\partial \alpha}(t, \mathbf{q}, 0)$ to be $\mathcal{C}^1$ with respect to $t$ and $\mathbf{q}$ ? I suspect this term is $\mathcal{C}^2$ with respect to $t$ and $\mathbf{q}$...

share|improve this question
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.