CONTENTS Introduction § 1. Results § 2. Preliminary results from mechanics § 3. Preliminary
results from mathematics § 4. The simplest problem of stability § 5. Contents of the paper …

An analysis of the normal forms to which functions can be reduced in neighbourhoods of
degenerate critical points shows that many of them are quasihomogeneous or …

CONTENTS Introduction § 1. Is there such a thing as symplectic topology? § 2. Generalizations
of the geometric theorem of Poincaré § 3. Hyperbolic Morse theory § 4. Intersections of …

In this text, the author constructs the mathematical apparatus of classical mechanics from the
beginning, examining all the basic problems in dynamics, including the theory of oscillations…

Recent progress in perturbation enables us to find many conditionally periodic motions in
every nonlinear dynamical system which is close to an integrable system (see [1,2]. The …

Recently VP Maslov gave a mathematically rigorous treatment of multidimensional asymptotic
methods of" quasiclassical" type in the large, ie, for any number of conjugate points [1, 2]. …

From the reviews of the first edition:"... In general the articles... are well written in a style that
enables one to grasp the ideas. The actual style is a readable mix of the important results, …

A straight line is just a Lagrangian subspace of the phase plane. The higher-dimensional
generalization of Sturm's theory, the account of which is given below, describes the evolution of …

7. Yu. S. Il'yashenko,“Analytic unsolvability of the stability problem and the problem of topological
classification of the singular points of analytic systems of differential equations”, Math. …

This paper contains a survey of research on critical points of smooth functions and their
bifurcations. We indicate applications to the theory of Lagrangian singularities (caustics), …