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Zero Level Perturbation of a Certain Third-Order Linear Solvable ODE with an Irregular Singularity at the Origin of Poincaré Rank 1
Springer Science and Business Media LLC - Tập 24 - Trang 511-539 - 2018
We study an irregular singularity of Poincaré rank 1 at the origin of a certain third-order linear solvable homogeneous ODE. We perturb the equation by introducing a small parameter
$\varepsilon \in ({\mathbb R}_{+},0)$
(ε < 1), which causes the ...... hiện toàn bộ
On Noncompact Minimal Sets of the Geodesic Flow
Springer Science and Business Media LLC - Tập 8 - Trang 47-64 - 2002
We study nontrivial (i.e., containing more than one orbit) minimal sets of the geodesic flow on Γ\T
1ℍ2, where Γ is a nonelementary Fuchsian group. It is not difficult to prove that nontrivial compact minimal sets always exist. We establish the existence of nontrivial noncompact minimal sets in two cases: (1) Γ is a Schottky group of special kind generated by infinitely many hyperbolic elements, (...... hiện toàn bộ
A Note on the Kepler Problem
Springer Science and Business Media LLC - Tập 8 - Trang 413-442 - 2002
J. Moser proved that the flow arising in the Kepler problem and restricted to the manifold of the constant energy E < 0 is equivalent to the geodesic flow on a sphere. This was proved by means of some algebraic manipulations with the Hamilton function. In a similar way Yu. S. Osipov proved that this flow is equivalent to the geodesic flow on the Euclidean space for E = 0 and on the Lobachevskii sp...... hiện toàn bộ
The De Casteljau Algorithm on Lie Groups and Spheres
Springer Science and Business Media LLC - Tập 5 - Trang 397-429 - 1999
We examine the De Casteljau algorithm in the context of Riemannian symmetric spaces. This algorithm, whose classical form is used to generate interpolating polynomials in
$$\mathbb{R}^n $$
, was also generalized to arbitrary Riemannian manifolds by others. However, the implementation of the generalized ...... hiện toàn bộ
On the Stokes Phenomenon of a Family of Multi-Perturbed Level-One Meromorphic Linear Differential Systems
Springer Science and Business Media LLC - Tập 19 Số 4 - Trang 575-592 - 2013
Time Optimal Control Problem of the 2D MHD Equations with Memory
Springer Science and Business Media LLC - Tập 29 - Trang 1323-1355 - 2023
In this paper, we study an optimal control problem for the 2D MHD equations with memory in bounded domains with Dirichlet boundary conditions, where the time needed to reach the desired state plays an essential role. We first prove the existence of optimal solutions. Then we establish the first-order necessary and second-order sufficient optimality conditions. The second-order optimality ones obta...... hiện toàn bộ
Integrable Weak Saddles for Trigonometric Liénard Systems
Springer Science and Business Media LLC - Tập 26 - Trang 551-556 - 2019
We give a complete algebraic characterization of the integrable weak saddles for planar trigonometric Liénard systems. The main tools used in our proof are the classification of the weak saddles on planar analytic Liénard systems and the characterization of some subfields of the quotient field of the ring of trigonometric polynomials.
Dynamical Analysis of the Generalized Lorenz Systems
Springer Science and Business Media LLC - Tập 23 - Trang 349-362 - 2016
In this paper, global attractive sets of the generalized Lorenz system are studied according to Lyapunov stability theory and optimization theory. The method of constructing Lyapunov functions applied to the former chaotic dynamical systems is not applicable to the generalized Lorenz system. We overcome this difficulty by adding a cross term to the Lyapunov functions of the generalized Lorenz syst...... hiện toàn bộ
Time Optimality for Systems with Multidimensional Control and Vector Moment Min-Problem
Springer Science and Business Media LLC - Tập 26 - Trang 525-550 - 2019
The linear time-optimal problem for some classes of linear systems with a multidimensional control is considered. The general position condition, which guarantees the uniqueness of the optimal control, is not assumed to be satisfied. We introduce a vector moment min-problem, which is a further development of the moment min-problem proposed by V.I. Korobov and G.M. Sklyar in 1987 for solving linear...... hiện toàn bộ
Exponential Stability of a Network of Beams
Springer Science and Business Media LLC - Tập 21 - Trang 443-460 - 2014
In this paper, we consider a network of elastic and thermoelastic Euler-Bernoulli beams. Our main result is to show that under certain conditions, the thermoelastic dissipation over some edges is sufficient to stabilize the whole system. Precisely, we establish the exponential stability of the network.
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