scientific article

Publication date: 23 January 1993

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

Lyapunov stability bifurcation invariant tori normalizing transformations existence of quasiperiodic solutions Hamiltonian and reversible systems nonlinear oscillations in multidimensional systems quasiperiodic motions in multidimensional nonlinear dynamical systems

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Bifurcation theory for ordinary differential equations (34C23) Hamilton's equations (70H05) Perturbations of ordinary differential equations (34D10) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Nonlinear dynamics in mechanics (70K99) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordinary differential equations (34-01) Almost and pseudo-almost periodic solutions to ordinary differential equations (34C27) Periodic and quasi-periodic flows and diffeomorphisms (37C55) Research exposition (monographs, survey articles) pertaining to ordinary differential equations (34-02)

Related Items

Non-algebraic integrability of the Chew-Low reversible dynamical system of the Cremona type and the relation with the 7th Hilbert problem (non-resonant case) ⋮ Attractors of the sine-Gordon equation in the field of a quasiperiodic external force ⋮ Unfoldings of quasi-periodic tori in reversible systems ⋮ Unnamed Item ⋮ The existence of quasiperiodic motions in quasilinear systems ⋮ Lyapunov stability of equilibrium states of reversible systems ⋮ Periodic solutions to nonlinear nonautonomous system of differential equations ⋮ Self-similar cycles and their local bifurcations in the problem of two weakly coupled oscillators ⋮ Algebraic-geometry approach to integrability of birational plane mappings. Integrable birational quadratic reversible mappings. I ⋮ Dynamical bifurcation of multifrequency oscillations in a fast-slow system ⋮ Unnamed Item ⋮ On the stability of integral manifolds of a system of ordinary differential equations in the critical case ⋮ On the existence and stability of business cycles in a dynamic model of a closed economy ⋮ Multifrequency oscillations of singularly perturbed systems ⋮ On the existence of tori in Asada's two-regional model ⋮ The reversible context 2 in KAM theory: the first steps ⋮ Nonzero periodic solutions of a special system of nonlinear differential equations ⋮ The dynamics of interaction by the money-commodities principle ⋮ Two-frequency autowave processes in the discrete Ginzburg-Landau equation ⋮ Perturbation theory of smooth invariant tori of dynamical systems ⋮ Bifurcation of an equilibrium for a system of differential equations in the critical case of two pure imaginary and two zero roots of the characteristic equation. I ⋮ Bifurcation of invariant tori in a neighborhood of an equilibrium of a system of ordinary differential equations ⋮ Forced resonant oscillations of nonlinear autonomous system in equilibrium neighborhood ⋮ On the existence of business cycles in Asada's two-regional model ⋮ Reversible systems with first integrals ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Invariant surfaces of periodic systems with conservative cubic first approximation ⋮ The Andronov-Hopf bifurcation with \(2:1\) resonance ⋮ Conservation and bifurcation of an invariant torus of a vector field ⋮ Dynamics of continuously controlling rod temperature as a singularly perturbed problem ⋮ On stability in Hamiltonian systems with two degrees of freedom ⋮ On the stability of the zero solution of a periodic reversible second-order differential equation ⋮ Two-frequency self-oscillations in a FitzHugh-Nagumo neural network