Isochronicity for several classes of Hamiltonian systems

DOI10.1006/jdeq.1999.3635zbMath0941.34017OpenAlexW2025529056MaRDI QIDQ1806154

Francesc Mañosas, Anna Cima, Jordi Villadelprat

Publication date: 20 December 1999

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.1999.3635

zbMATH Keywords

isochronous centerHamiltonian systems

Mathematics Subject Classification ID

Related Items (57)

Non-bifurcation of critical periods from semi-hyperbolic polycycles of quadratic centres ⋮ A characterization of isochronous centres in terms of symmetries. ⋮ On the classification of Liénard systems with amplitude-independent periods ⋮ Isochronicity for a class of reversible systems ⋮ Isochronicity for trivial quintic and septic planar polynomial Hamiltonian systems ⋮ Study of the period function of a two-parameter family of centers ⋮ Proof of the jacobian conjecture in the two-dimensional case and global isochronous centers of polynomial Hamiltonian differential systems ⋮ Global isochronous potentials ⋮ The period function of Hamiltonian systems with separable variables ⋮ On the upper bound of the criticality of potential systems at the outer boundary using the Roussarie-Ecalle compensator ⋮ A NOTE ON THE CRITICAL PERIODS OF POTENTIAL SYSTEMS ⋮ Commuting planar polynomial vector fields for conservative Newton systems ⋮ The center conditions and local bifurcation of critical periods for a Liénard system ⋮ Reachability of maximal number of critical periods without independence ⋮ The criticality of centers of potential systems at the outer boundary ⋮ Periodic perturbations of an isochronous center. ⋮ On the period function of centers in planar polynomial Hamiltonian systems of degree four. ⋮ Periodic oscillators, isochronous centers and resonance ⋮ Global determination of a nonlinearity from a periodic motion ⋮ Isochronous centers of polynomial Hamiltonian systems and a conjecture of Jarque and Villadelprat ⋮ Linearization of non-degenerate analytic centres in ⋮ Isochronous Oscillators ⋮ Analytic tools to bound the criticality at the outer boundary of the period annulus ⋮ Criticality via first order development of the period constants ⋮ Algebraic and analytical tools for the study of the period function ⋮ A note on the period function for certain planar vector fields ⋮ Two inverse problems for analytic potential systems ⋮ Period function and normalizers of vector fields in \(\mathbb R^n\) with \(n - 1\) first integrals ⋮ The period function of the generalized Lotka-Volterra centers ⋮ From isochronous potentials to isochronous systems ⋮ The period function and the harmonic balance method ⋮ Global existence of a restoring force realizing a prescribed half-period ⋮ Non-isochronicity of the center at the origin in polynomial Hamiltonian systems with even degree nonlinearities ⋮ New periodic recurrences with applications ⋮ The period function for quadratic integrable systems with cubic orbits ⋮ Non-isochronicity of the center in polynomial Hamiltonian systems ⋮ On the period function in a class of generalized Lotka-Volterra systems ⋮ On the return time function around monodromic polycycles ⋮ Complex planar Hamiltonian systems: linearization and dynamics ⋮ New lower bounds of the number of critical periods in reversible centers ⋮ On the period function of reversible quadratic centers with their orbits inside quartics ⋮ Period function monotonicity of planar vector fields ⋮ Criteria to bound the number of critical periods ⋮ On the isochronous center of planar piecewise polynomial potential systems ⋮ On the Topology of Isochronous Centers of Hamiltonian Differential Systems ⋮ Linearizability of planar polynomial Hamiltonian systems ⋮ Simultaneous bifurcation of limit cycles and critical periods ⋮ A proof of Bertrand's theorem using the theory of isochronous potentials ⋮ Existence and Homogenization of the Rayleigh-Bénard Problem ⋮ Period function for a class of Hamiltonian systems ⋮ On the reversible quadratic centers with monotonic period function ⋮ Nonexistence of isochronous centers in planar polynomial Hamiltonian systems of degree four ⋮ Isochronicity and linearizability of planar polynomial Hamiltonian systems ⋮ Isochronous centers and isochronous functions ⋮ Unnamed Item ⋮ The monotonicity of period function for the codimension four quadratic system \(Q_4\). ⋮ Involutions of real intervals

Cites Work

• Darboux linearization and isochronous centers with a rational first integral
• Isochronous centers of a linear center perturbed by fourth degree homogeneous polynomial
• On polynomial Hamiltonian planar vector fields
• The period function for Hamiltonian systems with homogeneous nonlinearities
• Linearization of isochronous centers
• The potential force yielding a periodic motion whose period is an arbitrary continuous function of the amplitude of the velocity
• Nonlinear oscillations of fixed period
• Isochronous Centers in Planar Polynomial Systems
• Bifurcation of Critical Periods for Plane Vector Fields
• Isochronicity of plane polynomial Hamiltonian systems
• A connection between isochronous Hamiltonian centres and the Jacobian Conjecture
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