On the approximation of dynamical indicators in systems with nonuniformly hyperbolic behavior [PDF]
Monatshefte für Mathematik, 2016 Let $f$ be a $C^{1+ }$ diffeomorphism of a compact Riemannian manifold and $ $ an ergodic hyperbolic measure with positive entropy. We prove that for every continuous potential $ $ there exists a sequence of basic sets $ _n$ such that the topological pressure $P(f| _n, )$ converges to the free energy $P_ ( ) = h( ) + \int {d }$.
openaire +2 more sources
Validity of numerical trajectories in the synchronization transition of complex systems [PDF]
, 2003 We investigate the relationship between the loss of synchronization and the onset of shadowing breakdown {\it via} unstable dimension variability in complex systems.
A. M. Batista +31 more
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New solutions of the soliton type of shallow water waves and superconductivity models
Results in Physics, 2023 For uni-directional wave transmission in the smooth bottom of shallow sea water and the superconductivity of nonlinear media with dispersion systems, the (1 + 1)-dimensional Camassa-Holm and Landau-Ginzburg-Higgs equations are of particular interest in ...
M. Ali Akbar +4 more
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Lagrangian Descriptors for Stochastic Differential Equations: A Tool for Revealing the Phase Portrait of Stochastic Dynamical Systems [PDF]
, 2016 In this paper we introduce a new technique for depicting the phase portrait of stochastic differential equations. Following previous work for deterministic systems, we represent the phase space by means of a generalization of the method of Lagrangian ...
Balibrea-Iniesta, Francisco +3 more
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Computability, Noncomputability, and Hyperbolic Systems [PDF]
, 2011 In this paper we study the computability of the stable and unstable manifolds of a hyperbolic equilibrium point. These manifolds are the essential feature which characterizes a hyperbolic system.
Buescu, Jorge +2 more
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Topology and Homoclinic Trajectories of Discrete Dynamical Systems [PDF]
, 2012 We show that nontrivial homoclinic trajectories of a family of discrete, nonautonomous, asymptotically hyperbolic systems parametrized by a circle bifurcate from a stationary solution if the asymptotic stable bundles Es(+{\infty}) and Es(-{\infty}) of ...
A. Abbondandolo +24 more
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A Novel Autonomous 5-D Hyperjerk RC Circuit with Hyperbolic Sine Function
The Scientific World Journal, 2018 A novel autonomous 5-D hyperjerk RC circuit with hyperbolic sine function is proposed in this paper. Compared to some existing 5-D systems like the 5-D Sprott B system, the 5-D Lorentz, and the Lorentz-like systems, the new system is the simplest 5-D ...
N. Tsafack, J. Kengne
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Transport in Transitory Dynamical Systems [PDF]
, 2010 We introduce the concept of a "transitory" dynamical system---one whose time-dependence is confined to a compact interval---and show how to quantify transport between two-dimensional Lagrangian coherent structures for the Hamiltonian case.
B. A. Mosovsky, J. D. Meiss, Kaper T. J.
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Spatial dynamics in the family of sixth-order differential equations from the theory of partial formation [PDF]
Известия высших учебных заведений: Прикладная нелинейная динамикаTopic of the paper. Bounded stationary (i.e. independent in time) spatially one-dimensional solutions of a quasilinear parabolic PDE are studied on the whole real line.
Kulagin, Nikolaj Evgenevich +1 more
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Skew products, quantitative recurrence, shrinking targets and decay of correlations
, 2011 We consider toral extensions of hyperbolic dynamical systems. We prove that its quantitative recurrence (also with respect to given observables) and hitting time scale behavior depend on the arithmetical properties of the extension.
Abadi +9 more
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