Roots of Unity and Unbounded Motions of an Asymmetric Oscillator
(R2?Z).The general questions that we have in mind are: under what conditions ona, b and f(t) can we say that (1) has unbounded solutions? are there equationsin the class (1) where unbounded and…
Periodic Solutions of a Newtonian Equation: Stability by the Third Approximation
- R. Ortega
- Mathematics
- 1 July 1996
Abstract This paper presents a sufficient condition for the stability of periodic solutions of a newtonian equation. This condition depends on the third order approximation and does not involve small…
Asymmetric Oscillators and Twist Mappings
- R. Ortega
- Mathematics
- 1 April 1996
Boundedness in a Piecewise Linear Oscillator and a Variant of the Small Twist Theorem
- R. Ortega
- Mathematics
- 1 September 1999
Consider the differential equation x¨+n2x+hL(x)=p(t),
Unbounded solutions of semilinear equations at resonance
We consider a forced harmonic oscillator at resonance with a nonlinear perturbation and obtain a sharp condition for the existence of unbounded motions. Such a condition is extended to the case of a…
The stability of the equilibrium of a nonlinear Hill's equation
- R. Ortega
- Mathematics
- 1 September 1994
Sufficient conditions for the stability of the trivial solution of a nonlinear Hill’s equation are obtained. As a consequence, the classical Lyapunov’s criterion for stability is extended to certain…
The index of lyapunov stable fixed points in two dimensions
- E. N. Dancer, R. Ortega
- Mathematics
- 1 October 1994
In this paper, we prove that a stable isolated fixed point of an orientation preserving local homeomorphism onR2 has fixed point index 1. We also give a number of applications to differential…
On the Families of Periodic Orbits of the Sitnikov Problem
The main goal of this paper is to study analytically the families of symmetric periodic orbits of the elliptic Sitnikov problem for all values of the eccentricity in the interval (0, 1), providing…
Some applications of the topological degree to stability theory
- R. Ortega
- Mathematics
- 1995
These notes are devoted to showing that the topological degree is a useful tool in the study of the properties of stability of periodic solutions of a scalar, time-dependent differential equation of…
A Maximum Principle for Periodic Solutions of the Telegraph Equation
- R. Ortega, A. Robles-Pérez
- Mathematics
- 15 May 1998
Let L s L u be a linear differential operator acting on functions u: V a R that are defined on a fixed manifold V. These functions will belong to a Ž . certain family B ; F V, R , and the definition…
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