Invariant manifolds and cluster synchronization in a family of locally coupled map lattices.
Invariant manifolds and the concept of asymptotic phase
Invariant manifolds of a differentiable vector field
Invariant measures and a stability theorem for locally Lipschitz stochastic delay equations
We consider a stochastic delay differential equation with exponentially stable drift and diffusion driven by a general Lévy process. The diffusion coefficient is assumed to be locally Lipschitz and bounded. Under a mild condition on the large jumps of the Lévy process, we show existence of an invariant measure. Main tools in our proof are a variation-of-constants formula and a stability theorem in our context, which are of independent interest.
Invariant measures for stochastic Cauchy problems with asymptotically unstable drift semigroup.
Invariant measures related with randomly connected Poisson driven differential equations
We consider the stochastic differential equation (1) for t ≥ 0 with the initial condition u(0) = x₀. We give sufficient conditions for the existence of an invariant measure for the semigroup corresponding to (1). We show that the existence of an invariant measure for a Markov operator P corresponding to the change of measures from jump to jump implies the existence of an invariant measure for the semigroup describing the evolution of measures along trajectories and vice versa.
Invariant sets for semilinear parabolic and elliptic systems
Invariant tori for periodically perturbed oscillators.
The response of an oscillator to a small amplitude periodic excitation is discussed. In particular, sufficient conditions are formulated for the perturbed oscillator to have an invariant torus in the phase cylinder. When such an invariant torus exists, some perturbed solutions are in the basin of attraction of this torus and are thus entrained to the dynamical behavior of the perturbed system on the torus. In particular, the perturbed solutions in the basin of attraction of the invariant torus are...
Invariant transformations for the Sturm--Liouville operator.
Invariants of kinetic differential equations.
Inverse differentiability contractors and equations in Banach spaces
Inverse monotonicity and difference schemes of higher order. A summary for two-point boundary value problems.
Inverse nodal problems for the Sturm-Liouville differential operators on a star-type graph.
Inverse problems connected with periods of oscillations described by ẍ + g(x) = 0
Inverse problems in the theory of analytic planar vector fields.
In this communication we state and analyze the new inverse problems in the theory of differential equations related to the construction of an analytic planar verctor field from a given, finite number of solutions, trajectories or partial integrals.Likewise, we study the problem of determining a stationary complex analytic vector field Γ from a given, finite subset of terms in the formal power series (...).
Inverse problems on star-type graphs: differential operators of different orders on different edges
We study inverse spectral problems for ordinary differential equations on compact star-type graphs when differential equations have different orders on different edges. As the main spectral characteristics we introduce and study the so-called Weyl-type matrices which are generalizations of the Weyl function (m-function) for the classical Sturm-Liouville operator. We provide a procedure for constructing the solution of the inverse problem and prove its uniqueness.
Inverse scattering for the one-dimensional Stark effect and application to the cylindrical KdV equation
Inverse spectral analysis for singular differential operators with matrix coefficients.
Inverse spectral problems for nonlinear Sturm-Liouville problems.
Inversion in indirect optimal control of multivariable systems
This paper presents the role of vector relative degree in the formulation of stationarity conditions of optimal control problems for affine control systems. After translating the dynamics into a normal form, we study the Hamiltonian structure. Stationarity conditions are rewritten with a limited number of variables. The approach is demonstrated on two and three inputs systems, then, we prove a formal result in the general case. A mechanical system example serves as illustration.