14 citations · 59 across the 15 of their papers we have counts for
15 papers
Nonlinear constrained optimization of Schur test functions
Mikhail Anikushin, Andrey Romanov
We apply the iterative nonlinear programming method, previously proposed in our earlier work, to optimize Schur test functions and thereby provide refined upper bounds for the norm…
Robust upper estimates for topological entropy via nonlinear constrained optimization over adapted metrics
Mikhail Anikushin, Andrey Romanov
We present an analytical-numerical method providing robust upper estimates for the topological entropy or, more generally, uniform volume growth exponents of differentiable mapping…
Frequency conditions for the global stability of nonlinear delay equations with several equilibria
Mikhail Anikushin, Andrey Romanov
In our adjacent work, we developed a spectral comparison principle for compound cocycles generated by delay equations. It allows to derive frequency inequalities for the uniform ex…
Variational description of uniform Lyapunov exponents via adapted metrics on exterior products
Mikhail Anikushin
In this work, we present a comprehensive study of the relationship among uniform Lyapunov exponents, the Liouville trace formula, and adapted metrics for cocycles in Hilbert spaces…
Spectral comparison of compound cocycles generated by delay equations in Hilbert spaces
Mikhail Anikushin
We study linear cocycles generated by nonautonomous delay equations in a suitable Hilbert space and their extensions, called compound cocycles, to exterior powers. Using a recent v…
Hidden and unstable periodic orbits as a result of homoclinic bifurcations in the Suarez-Schopf delayed oscillator and the irregularity of ENSO
Mikhail Anikushin, Andrey Romanov
We revisit the classical Suarez-Schopf delayed oscillator. Special attention is paid to the region of linear stability in the space of parameters. By means of the theory of inertia…
Inertial manifolds and foliations for asymptotically compact cocycles in Banach spaces
Mikhail Anikushin
We study asymptotically compact nonautonomous dynamical systems given by abstract cocycles in Banach spaces. Our main assumptions are given by a squeezing property in a quadratic c…
Frequency theorem for parabolic equations and its relation to inertial manifolds theory
Mikhail Anikushin
We obtain a version of the Frequency Theorem (a theorem on solvability of certain operator inequalities), which allows to construct quadratic Lyapunov functionals for semilinear pa…
Nonlinear semigroups for delay equations in Hilbert spaces, inertial manifolds and dimension estimates
Mikhail Anikushin
We study the well-posedness of nonautonomous nonlinear delay equations in as evolutionary equations in a proper Hilbert space. We present a construction of solving…
Frequency theorem and inertial manifolds for neutral delay equations
Mikhail Anikushin
We study the quadratic regulator problem for linear control systems in Hilbert spaces, where the cost functional is in some sense unbounded. Our motivation comes from delay equatio…
The Poincaré-Bendixson theory for certain compact semi-flows in Banach spaces
Mikhail Anikushin
We study semiflows satisfying a certain squeezing condition with respect to a quadratic functional in some Banach space. Under certain compactness assumptions from our previous res…
A non-local reduction principle for cocycles in Hilbert spaces
Mikhail Anikushin
We study cocycles (non-autonomous dynamical systems) satisfying a certain squeezing condition with respect to the quadratic form of a bounded self-adjoint operator acting in a Hilb…
On the Dimensional-like Characteristics Arising From Linear Inhomogeneous Approximations
Mikhail Anikushin
As it follows from the theory of almost periodic functions the set of integer solutions to the Kronecker system , , where…
Dimension Theory Approach to the Complexity of Almost Periodic Trajectories
Mikhail Anikushin
We introduce and study a dimensional-like characteristic of an uniformly almost periodic function, which we call the Diophantine dimension. By definition, it is the exponent in the…
Badly Approximable Numbers and the Growth Rate of the Inclusion Length of an Almost Periodic Function
Mikhail Anikushin
We study the growth rate of the inclusion length of an almost periodic function. For a given a. p. function such growth rate depends on the algebraic structure of Fourier exponents…