Supriyo Jana

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math.DS2026

Darboux first integrals of Kolmogorov systems with invariant $n$ -sphere

Supriyo Jana, Soumen Sarkar

In this paper, we characterize all polynomial Kolmogorov vector fields for which the standard $n$ -sphere is invariant. We exhibit completely integrable Kolmogorov vector fields of…

math.DS2024

Dynamics and integrability of polynomial vector fields on the $n$ -dimensional sphere

Supriyo Jana, Soumen Sarkar

In this paper, we characterize arbitrary polynomial vector fields on $S^{n}$ . We establish a necessary and sufficient condition for a degree one vector field on the odd-dimensional s…

math.DS2024

Characterization and dynamics of certain classes of polynomial vector fields on the torus

Supriyo Jana

In this paper, we classify all polynomial vector fields in $R^{3}$ of degree up to three such that their flow makes the torus $$\mathbb{T}^2=\{(x,y,z)\in \mathbb{R}^3:(x^2+y…

Darboux first integrals of Kolmogorov systems with invariant n-sphere

Dynamics and integrability of polynomial vector fields on the n-dimensional sphere

Characterization and dynamics of certain classes of polynomial vector fields on the torus

Darboux first integrals of Kolmogorov systems with invariant $n$ -sphere

Dynamics and integrability of polynomial vector fields on the $n$ -dimensional sphere