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International Journal of Bifurcation and Chaos, ISSN 0218-1274, 09/2017, Volume 27, Issue 10, p. 1750164
Definitions of Hausdorff–Lebesgue measure and dimension are introduced. Combination of Hausdorff and Lebesgue ideas are used. Methods for upper and lower... 
Lorenz system | fractal | attractors | Hausdorff-Lebesgue | Hausdorff | dimension | Lyapunov | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTIDISCIPLINARY SCIENCES | Mathematics - Dynamical Systems
Journal Article
Physics Letters A, ISSN 0375-9601, 06/2016, Volume 380, Issue 25-26, pp. 2142 - 2149
Journal Article
Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 12/2016, Volume 41, pp. 84 - 103
Journal Article
Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 04/2014, Volume 19, Issue 4, pp. 1027 - 1034
Journal Article
Nonlinear Dynamics, ISSN 0924-090X, 7/2016, Volume 85, Issue 1, pp. 195 - 201
Journal Article
International Journal of Bifurcation and Chaos, ISSN 0218-1274, 12/2016, Volume 26, Issue 14, p. 1650240
New classes of Lyapunov-type functions are suggested for the estimation of Lyapunov dimension of Lorenz-like systems. Lyapunov dimension formulas for Lorenz... 
Attractors of dynamical systems | fractal dimension | Hausdorff dimension | Lyapunov dimension | Lorenz and Tigan systems | Lyapunov-Type functions | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Lyapunov-type functions | MULTIDISCIPLINARY SCIENCES | TIME | CHAOTIC ATTRACTORS | ENTROPY
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 12/2018, Volume 86, pp. 264 - 269
A De La Vallée Poussin-type inequality is established for a certain class of partial differential equations posed in a bounded domain Ω in RN+1, N≥1, under... 
Sign-changing criteria | Higher dimension | De La Vallée Poussin-type inequalities | LYAPUNOV-TYPE INEQUALITIES | MATHEMATICS, APPLIED | SIGN-CHANGING SOLUTIONS | De La Vallee Poussin-type inequalities
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 03/2020, Volume 268, Issue 7, pp. 3497 - 3563
The FitzHugh-Nagumo (FHN) equation is a simplified model of a nerve axon. We explore the controllability of this model using a localized interior control only... 
Rogers-McCulloch model | Lyapunov functional | Approximate controllability | Pole shifting | FHN equation | Riesz basis | SYSTEM | MATHEMATICS | FEEDBACK STABILIZATION | HEAT-EQUATION | STATE | MONODOMAIN EQUATIONS
Journal Article
Chaos: An Interdisciplinary Journal of Nonlinear Science, ISSN 1054-1500, 04/2018, Volume 28, Issue 4, p. 041103
We show how to obtain theoretical and numerical estimates of correlation dimension and phase space contraction by using the extreme value theory. The maxima of... 
MATHEMATICS, APPLIED | NORTH-ATLANTIC OSCILLATION | LYAPUNOV EXPONENTS | RARE EVENTS | GENERALIZED HENON MAPS | DYNAMICAL-SYSTEMS | STATISTICS | SETS | TIME-SERIES | PHYSICS, MATHEMATICAL | TRENDS | Physics - Chaotic Dynamics | Dynamical Systems | Mathematics
Journal Article
Journal of Sound and Vibration, ISSN 0022-460X, 07/2016, Volume 373, pp. 192 - 204
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 01/2016, Volume 144, Issue 1, pp. 119 - 128
This paper provides the Hausdorff dimension estimation for an ergodic hyperbolic measure of C^1-dimensional compact Riemannian manifold with the assumption... 
DIFFEOMORPHISMS | MATHEMATICS | MATHEMATICS, APPLIED | entropy | Lyapunov exponents | dominated splitting | Dimension
Journal Article
NONLINEARITY, ISSN 0951-7715, 02/2020, Volume 33, Issue 2, pp. 790 - 806
In this article we study the regularity of the topological and metric entropy of partially hyperbolic flows with two-dimensional center direction. We show that... 
topological entropy | entropy measure | VOLUME GROWTH | ERGODICITY | MATHEMATICS, APPLIED | LYAPUNOV EXPONENTS | ANOSOV | partially hyperbolic flows | PHYSICS, MATHEMATICAL | TOPOLOGICAL-ENTROPY
Journal Article
Physics Letters A, ISSN 0375-9601, 2011, Volume 375, Issue 8, pp. 1179 - 1182
An analytical formula for the Lyapunov dimension of the Lorenz attractor is presented under assumption that all the equilibria are unstable. 
Lorenz system | Lyapunov dimension | PHYSICS, MULTIDISCIPLINARY | Solid state physics | Mathematical analysis
Journal Article
International Journal of Bifurcation and Chaos, ISSN 0218-1274, 11/2015, Volume 25, Issue 12, p. 1530036
This paper describes two simple three-dimensional autonomous chaotic flows whose attractor dimensions can be adjusted continuously from 2 . 0 to 3 . 0 by a... 
Chaos | low-dimensional chaos | differential equation | conservative system | dynamical system | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTIDISCIPLINARY SCIENCES | Jacobian matrix | Lyapunov exponents | Chaos theory | Dissipation | Eigenvalues | Electronics | Bifurcations | Three dimensional
Journal Article