Two Soviet Studies on Frege

Many problems in celestial mechanics physics and engineering involve the studyof oscillating systems governed by nonlinear ordinary differential equations orpar... » 

Many problems in celestial mechanics physics and engineering involve the studyof oscillating systems governed by nonlinear ordinary differential equations orpartial differential equations. This volume represents an importantcontribution to the available methods of solution for such systems. Thecontents are divided into six chapters. Chapter 1 presents a study of periodicsolutions for nonlinear systems of evolution equations including differentialequations with lag systems of neutral type various classes of nonlinearsystems of integrodifferential equations etc. A numericalanalytic method forthe investigation of periodic solutions of these evolution equations ispresented. In Chapters 2 and 3 problems concerning the existence of periodicand quasiperiodic solutions for systems with lag are examined. For a nonlinearsystem with quasiperiodic coefficients and lag the conditions under whichquasiperiodic solutions exist are established. Chapter 4 is devoted to thestudy of invariant toroidal manifolds for various classes of systems ofdifferential equations with quasiperiodic coefficients. Chapter 5 examines theproblem concerning the reducibility of a linear system of difference equationswith quasiperiodic coefficients to a linear system of difference equations withconstant coefficients. Chapter 6 contains an investigation of invarianttoroidal sets for systems of difference equations with quasiperiodiccoefficients. For mathematicians whose work involves the study of oscillatingsystems. «