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Symmetry-Driven $k$-Essence Cosmological Dynamics
We investigate a family of $k$-essence cosmological models selected by the requirement that the field equations admit a nontrivial variational symmetry. For the $k$-essence theory with Lagrangian function $F(R,X,ϕ)=f_{1}R+f_{2}(ϕ,X)$, where $f_{2}(ϕ,X)=αX+β\exp\left((n-1)ϕ\right)X^{n}$, the existenc
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