Cover

Title page

Contents

Preface

Program

Photos

From Hilbert’s superposition problem to dynamical systems

Recollections

Symplectization, complexification and mathematical trinities

Topological problems in wave propagation theory and topological economy principle in algebraic geometry

Geometry and control of three-wave interactions

Standard basis along a Samuel stratum, and implicit differentiation

A global weighted version of Bezout’s theorem

Real Enriques surfaces without real points and Enriques-Einstein-Hitchin 4-manifolds

On the index of a vector field at an isolated singularity

The exponential map on 𝒟^{𝓈}_{𝜇}

Zeldovich’s neutron star and the prediction of magnetic froth

Arnold conjecture and Gromov-Witten invariant for general symplectic manifolds

Multiplicity of a zero of an analytic function on a trajectory of a vector field

Singularity theory and symplectic topology

On enumeration of meromorphic functions on the line

Pseudoholomorphic curves and dynamics

Bifurcation of planar and spatial polycycles: Arnold’s program and its development

Singularity which has no 𝑀-smoothing

Symplectic geometry on moduli spaces of holomorphic bundles over complex surfaces

Newton polyhedra, a new formula for mixed volume, product of roots of a system of equations

Interactions of Andronov-Hopf and Bogdanov-Takens bifurcations

Solutions of the qKZB equation in tensor products of finite dimensional modules over the elliptic quantum group 𝐸_{𝜏,𝜂}𝑠𝑙₂

Schrodinger operators on graphs and symplectic geometry

On the dominant Fourier modes in the series associated with separatrix splitting for an a-priori stable, three degree-of-freedom Hamiltonian system

Homology of 𝑖-connected graphs and invariants of knots, plane arrangements, etc.

On Arnold’s variational principles in fluid mechanics

On functions and curves defined by ordinary differential equations

Global finiteness properties of analytic families and algebra of their Taylor coefficients

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