Monotonicity of the period function for planar Hamiltonian vector fields: A Generalization of Chicone's Criterion
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918237945462784 |
|---|---|
| author | Nascimento, F. J. S. |
| author_facet | Nascimento, F. J. S. |
| contents | This paper investigates the monotonicity of the period function associated with planar Hamiltonian systems of the form $H(x,y) = F(x) + G(y)$. We establish sufficient conditions ensuring the monotonicity of the period function corresponding to a nondegenerate center, expressed explicitly in terms of the functions F and G. Our approach extends Chicone's classical criterion, originally formulated for systems of the type $x' = y$, $y' = -F'(x)$, to a broader Hamiltonian framework. As a main application, we analyze the monotonicity of the period function associated with the center at (0,0) of the polynomial Hamiltonian system $$H(x,y) = (1/2)x^2 + (a/3)x^3 + (b/4)x^4 + (1/2)y^2 + (c/4)y^4,$$ as a function of the parameters $a, b, c \in \mathbb{R}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07556 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Monotonicity of the period function for planar Hamiltonian vector fields: A Generalization of Chicone's Criterion Nascimento, F. J. S. Dynamical Systems Classical Analysis and ODEs This paper investigates the monotonicity of the period function associated with planar Hamiltonian systems of the form $H(x,y) = F(x) + G(y)$. We establish sufficient conditions ensuring the monotonicity of the period function corresponding to a nondegenerate center, expressed explicitly in terms of the functions F and G. Our approach extends Chicone's classical criterion, originally formulated for systems of the type $x' = y$, $y' = -F'(x)$, to a broader Hamiltonian framework. As a main application, we analyze the monotonicity of the period function associated with the center at (0,0) of the polynomial Hamiltonian system $$H(x,y) = (1/2)x^2 + (a/3)x^3 + (b/4)x^4 + (1/2)y^2 + (c/4)y^4,$$ as a function of the parameters $a, b, c \in \mathbb{R}$. |
| title | Monotonicity of the period function for planar Hamiltonian vector fields: A Generalization of Chicone's Criterion |
| topic | Dynamical Systems Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2512.07556 |