Monotonicity of the Period Function in Planar Separable Hamiltonian Systems: An Extension of Chicone’s Criterion
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2026-09-17
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Campus
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We investigate the monotonicity of the period function associated with planar Hamiltonian systems of the form H(x, y) = F(x) + G(y), where G is an even function. We derive explicit sufficient conditions, expressed solely in terms of the functions F, G, and their derivatives, ensuring the monotonicity of the period function associated with a nondegenerate center. Our results extend Chicone’s classical criterion, originally established for potential systems, to a broader class of separable Hamiltonian systems. The effectiveness of the proposed criterion is illustrated through applications including polynomial, trigonometric, hyperbolic and relativistic Hamiltonian systems.