Search results for " Dynamical systems"
showing 5 items of 165 documents
Complex dynamics, hidden attractors and continuous approximation of a fractional-order hyperchaotic PWC system
2018
In this paper, a continuous approximation to studying a class of PWC systems of fractionalorder is presented. Some known results of set-valued analysis and differential inclusions are utilized. The example of a hyperchaotic PWC system of fractional order is analyzed. It is found that without equilibria, the system has hidden attractors.
Ledrappier-Young formula and exact dimensionality of self-affine measures
2017
In this paper, we solve the long standing open problem on exact dimensionality of self-affine measures on the plane. We show that every self-affine measure on the plane is exact dimensional regardless of the choice of the defining iterated function system. In higher dimensions, under certain assumptions, we prove that self-affine and quasi self-affine measures are exact dimensional. In both cases, the measures satisfy the Ledrappier-Young formula. peerReviewed
On several notions of complexity of polynomial progressions
2021
For a polynomial progression $$(x,\; x+P_1(y),\; \ldots,\; x+P_{t}(y)),$$ we define four notions of complexity: Host-Kra complexity, Weyl complexity, true complexity and algebraic complexity. The first two describe the smallest characteristic factor of the progression, the third one refers to the smallest-degree Gowers norm controlling the progression, and the fourth one concerns algebraic relations between terms of the progressions. We conjecture that these four notions are equivalent, which would give a purely algebraic criterion for determining the smallest Host-Kra factor or the smallest Gowers norm controlling a given progression. We prove this conjecture for all progressions whose ter…
Lyapunov quantities and limit cycles in two-dimensional dynamical systems : analytical methods, symbolic computation and visualization
2011
Acoustic wave guides as infinite-dimensional dynamical systems
2015
We prove the unique solvability, passivity/conservativity and some regularity results of two mathematical models for acoustic wave propagation in curved, variable diameter tubular structures of finite length. The first of the models is the generalised Webster's model that includes dissipation and curvature of the 1D waveguide. The second model is the scattering passive, boundary controlled wave equation on 3D waveguides. The two models are treated in an unified fashion so that the results on the wave equation reduce to the corresponding results of approximating Webster's model at the limit of vanishing waveguide intersection.