Rigid Polynomial Differential Systems with Homogeneous Nonlinearities

Jaume Llibre

doi:10.20944/preprints202407.1946.v1

Preprint Article Version 1 This version is not peer-reviewed

Version 1 : Received: 23 July 2024 / Approved: 24 July 2024 / Online: 24 July 2024 (11:43:22 CEST)

Planar differential systems whose angular velocity is constant are called rigid differential systems. We characterize the existence and non-existence of limit cycles, and the finite and infinite singularities of the rigid polynomial differential systems with homogeneous nonlinearities of arbitrary degree in the Poincaré disc. Moreover, we classify the phase portraits in the Poincaré disc of the rigid polynomial differential systems of degree two, and of one class of rigid polynomial differential systems with cubic homogeneous nonlinearitie that can exhibit one limit cycle.

quadratic systems; quadratic differential systems; limit cycles; rigid system; rigid differntial systems

Computer Science and Mathematics, Analysis

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Rigid Polynomial Differential Systems with Homogeneous Nonlinearities

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