Gap-bifurcation for nonlinear perturbations of Hill's equation.
General boundedness theorems to some second order nonlinear differential equation with integrable forcing term.
General linear methods: connection to one step methods and invariant curves.
Generalization of amplitude phase and accompanying differential equation
Generalization of the theorem on the argument of almost periodic function
Generalized Hopf bifurcations and applications to planar quadratic systems
Generalized linking theorem and nonlinear equations in unbounded domains
Generalized nonlinear superposition principles for polynomial planar vector fields.
Generalized Picone's formula and forced oscillations in quasilinear differential equations of the second order
In the paper a comparison theory of Sturm-Picone type is developed for the pair of nonlinear second-order ordinary differential equations first of which is the quasilinear differential equation with an oscillatory forcing term and the second is the so-called half-linear differential equation. Use is made of a new nonlinear version of the Picone’s formula.
Generalized reciprocity for self-adjoint linear differential equations
Let , be an -th order differential operator, be its adjoint and be positive functions. It is proved that the self-adjoint equation is nonoscillatory at if and only if the equation is nonoscillatory at . Using this result a new necessary condition for property BD of the self-adjoint differential operators with middle terms is obtained.
Generalized Sturm-Liouville equations
Generalized Sturm-Liouville equations. II
Generalized synchronization in a system of several non-autonomous oscillators coupled by a medium
An abstract theory on general synchronization of a system of several oscillators coupled by a medium is given. By generalized synchronization we mean the existence of an invariant manifold that allows a reduction in dimension. The case of a concrete system modeling the dynamics of a chemical solution on two containers connected to a third container is studied from the basics to arbitrary perturbations. Conditions under which synchronization occurs are given. Our theoretical results are complemented...
Generation of nonlinear ordinary differential equations with given Lie algebra of point symmetries. (Erzeugung nichtlinearer gewöhnlicher Differentialgleichungen mit vorgegebener Lie-Algebra von Punktsymmetrien.)
Generic bifurcation of reversible vector fields on a 2-bidimensional manifold.
In this paper we deal with reversible vector fields on a 2-dimensional manifold having a codimension one submanifold as its symmetry axis. We classify generically the one parameter families of such vector fields. As a matter of fact, aspects of structural stability and codimension one bifurcation are analysed.
Generic bifurcations of second order ordinary differential equations on differentiable manifolds
Generic measures for geodesic flows on nonpositively curved manifolds
We study the generic invariant probability measures for the geodesic flow on connected complete nonpositively curved manifolds. Under a mild technical assumption, we prove that ergodicity is a generic property in the set of probability measures defined on the unit tangent bundle of the manifold and supported by trajectories not bounding a flat strip. This is done by showing that Dirac measures on periodic orbits are dense in that set.In the case of a compact surface, we get the following sharp result:...
Generic saddle-node bifurcation for cascade second order ODEs on manifolds
Cascade second order ODEs on manifolds are defined. These objects are locally represented by coupled second order ODEs such that any solution of one of them can represent an external force for the other one. A generic saddle-node bifurcation theorem for 1-parameter families of cascade second order ODEs is proved.
Geometric linearization of ordinary differential equations.
Geometry of third order ODE systems
We compute cohomology spaces of Lie algebras that describe differential invariants of third order ordinary differential equations. We prove that the algebra of all differential invariants is generated by 2 tensorial invariants of order 2, one invariant of order 3 and one invariant of order 4. The main computational tool is a Serre-Hochschild spectral sequence and the representation theory of semisimple Lie algebras. We compute differential invariants up to degree 2 as application.