Dynamical analysis of $k$-essence cosmology in the light of Supernova Ia observations

In this paper, we analyse the JLA data on Supernova observations in the context of $k-$essence dark energy model with Lagrangian $L=VF(X)$, with a constant potential $V$ and the dynamical term $X = (1/2)\nabla_{\mu}\phi\nabla_{\nu}\phi = \dot{\phi}^2/2$ for a homogeneous scalar field $\phi(t)$, in a flat FRW spacetime background. Scaling relations are used to extract temporal behaviour of different cosmological quantities and the form of the function $F(X)$ from the data. We explore how the parameters of the model, viz. value of the constant potential $V$ and a constant $C$ appearing in the emergent scaling relation, control the dynamics of the model in the context of JLA data, by setting up and analysing an equivalent dynamical system described by a set of autonomous equations.