On integrability of the Nosé-Hoover oscillator and generalized Nosé-Hoover oscillator

Symmetries, invariants of ordinary differential equations (34C14) Explicit solutions, first integrals of ordinary differential equations (34A05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Cites Work

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Integrability of dynamical systems: algebra and analysis
Integrability of the Nosé-Hoover equation
Galoisian obstructions to non-Hamiltonian integrability
Invariant algebraic surfaces for generalized Raychaudhuri equations
Non-ergodicity of the Nosé-Hoover thermostatted harmonic oscillator
Multiplicity of invariant algebraic curves in polynomial vector fields
Global analytic integrability of the Rabinovich system
Global dynamics of the Rikitake system
Analytic first integrals of the FitzHugh-Nagumo systems
An algorithm for solving second order linear homogeneous differential equations
Extended integrability and bi-Hamiltonian systems
Local first integrals of differential systems and diffeomorphisms
Integrable geodesic flows with positive topological entropy
Darboux integrability of the Lü system
Global dynamics and bifurcation of periodic orbits in a modified Nosé-Hoover oscillator
Integrability analysis of the stretch-twist-fold flow
Kovalevskaya exponents, weak Painlevé property and integrability for quasi-homogeneous differential systems
Ergodicity of a singly-thermostated harmonic oscillator
Integrability analysis of the Shimizu-Morioka system
Invariant algebraic surfaces and algebraic first integrals of the Maxwell-Bloch system
Integrability analysis of chaotic and hyperchaotic finance systems
Qualitative theory of planar differential systems
The second law of thermodynamics and multifractal distribution functions: bin counting, pair correlations, and the Kaplan-Yorke conjecture
Darboux polynomials and global phase portraits for the $D_{2}$ vector field
Bi-Hamiltonian Structures of 3D Chaotic Dynamical Systems
GLOBAL DYNAMICS OF THE LORENZ SYSTEM WITH INVARIANT ALGEBRAIC SURFACES
Bounded Polynomial Vector Fields
Some third-order ordinary differential equations
Dynamics of the Lorenz system having an invariant algebraic surface
Dynamical systems and Poisson structures
Dynamics at infinity and the existence of singularly degenerate heteroclinic cycles in the Lorenz system
Galois groups and elementary solutions of some linear differential equations.
Group-theoretic obstructions to integrability
Galoisian obstructions to integrability and Melnikov criteria for chaos in two-degree-of-freedom Hamiltonian systems with saddle centres
Invariant Algebraic Surfaces and Hopf Bifurcation of a Finance Model
Nonintegrability of the unfolding of the fold-Hopf bifurcation
Formal and analytic integrability of the Lorenz system
Invariant algebraic surfaces of the Lorenz system
Differential Galois integrability obstructions for nonlinear three-dimensional differential systems
Meromorphic and formal first integrals for the Lorenz system
Non-integrability of the optimal control problem for n-level quantum systems
On the integrability of the $5$-dimensional Lorenz system for the gravity-wave activity
The Coexistence of Invariant Tori and Topological Horseshoe in a Generalized Nosé–Hoover Oscillator
Differential Galois theory and non-integrability of Hamiltonian systems

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