Evolution maps and center manifolds
Sign Up to like & getrecommendations! Published in 2020 at "Aequationes mathematicae"
DOI: 10.1007/s00010-020-00728-z
Abstract: We use evolution maps to construct center-stable, center-unstable and center invariant manifolds with optimal regularity for a nonautonomous dynamics with discrete time. The proofs comprise essentially two steps: first we reformulate the original problem in… read more here.
Keywords: maps center; center manifolds; center; evolution maps ... See more keywords
Nonmonotone invariant manifolds in the Nagylaki–Crow model
Sign Up to like & getrecommendations! Published in 2018 at "Nonlinear Analysis: Real World Applications"
DOI: 10.1016/j.nonrwa.2017.11.011
Abstract: Abstract We use a change of dynamical variables to prove, subject to certain conditions on the parameters, that a nonmonotone invariant manifold exists and is the graph of a convex function for the planar Nagylaki–Crow… read more here.
Keywords: nagylaki crow; manifolds nagylaki; model; nonmonotone invariant ... See more keywords
A Wong-Zakai approximation for random invariant manifolds
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DOI: 10.1063/1.5017932
Abstract: Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic influences. But these random objects are difficult to be visualized geometrically or computed numerically. The current work provides a perturbation approach to… read more here.
Keywords: random invariant; invariant manifold; zakai approximation; random ... See more keywords
On the dynamics of the Euler equations on so(4)
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DOI: 10.1080/14689367.2019.1703906
Abstract: This paper deals with the Euler equations on the Lie Algebra so(4). These equations are given by a polynomial differential system in . We prove that this differential system has four 3-dimensional invariant manifolds and… read more here.
Keywords: euler equations; dynamics euler; invariant manifolds;
Unstable equilibria and invariant manifolds in quasi-two-dimensional Kolmogorov-like flow.
Sign Up to like & getrecommendations! Published in 2018 at "Physical Review E"
DOI: 10.1103/physreve.98.023105
Abstract: Recent studies suggest that unstable, nonchaotic solutions of the Navier-Stokes equation may provide deep insights into fluid turbulence. In this article, we present a combined experimental and numerical study exploring the dynamical role of unstable… read more here.
Keywords: unstable equilibria; two dimensional; equilibria invariant; flow ... See more keywords
Embedding the Dynamics of Forced Nonlinear Systems in Multistable Memristor Circuits
Sign Up to like & getrecommendations! Published in 2022 at "IEEE Journal on Emerging and Selected Topics in Circuits and Systems"
DOI: 10.1109/jetcas.2022.3220363
Abstract: A well-known feature of memristors is that they makes the circuit dynamics much richer than that generated by classical $RLC$ circuits containing nonlinear resistors. In the case of circuits with ideal memristors, such a multistability… read more here.
Keywords: invariant manifolds; circuit; forced nonlinear; memristor ... See more keywords
Heteroclinic Transition Motions in Periodic Perturbations of Conservative Systems with an Application to Forced Rigid Body Dynamics
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DOI: 10.1134/s1560354718040056
Abstract: We consider periodic perturbations of conservative systems. The unperturbed systems are assumed to have two nonhyperbolic equilibria connected by a heteroclinic orbit on each level set of conservative quantities. These equilibria construct two normally hyperbolic… read more here.
Keywords: conservative systems; perturbations conservative; transition motions; periodic orbits ... See more keywords
The Casson–Walker invariant of 3-manifolds with genus one open book decompositions
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Knot Theory and Its Ramifications"
DOI: 10.1142/s0218216519500184
Abstract: In this paper, we give two formulae of values of the Casson–Walker invariant of 3-manifolds with genus one open book decompositions; one is a formula written in terms of a framed link of a surgery… read more here.
Keywords: manifolds genus; open book; walker invariant; casson walker ... See more keywords
Orthogonal Approximation of Invariant Manifolds in the Circular Restricted Three-Body Problem
Sign Up to like & getrecommendations! Published in 2023 at "Journal of Guidance, Control, and Dynamics"
DOI: 10.2514/1.g007304
Abstract: Methods to parameterize and approximate the hyperbolic invariant manifolds of particular solutions in the circular restricted three-body problem (CR3BP) are presented in this paper. Analytical representations obtained from these manifold approximations are instrumental in the… read more here.
Keywords: problem; three body; invariant manifolds; body problem ... See more keywords
On motions of a conservative system on invariant manifolds
Sign Up to like & getrecommendations! Published in 2018 at "Cybernetics and Physics"
DOI: 10.35470/2226-4116-2018-7-3-130-143
Abstract: In [Irtegov and Burlakova, 2017], the algorithms for the qualitative analysis of conservative systems have been presented. These are based on the Routh-Lyapunov method [Lyapunov, 1954] and some its modifications [Irtegov and Titorenko, 2009] as… read more here.
Keywords: space; system invariant; conservative system; motions conservative ... See more keywords