Results 21 to 30 of about 1,473,692 (365)
Convergence time towards periodic orbits in discrete dynamical systems. [PDF]
PLoS ONE, 2014 We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we use ...
Jesús San Martín, Mason A Porter
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An optimal gains matrix for time-delay feedback control [PDF]
, 2009 In this paper we propose an optimal time-delayed feedback control (TDFC) for tracking unstable periodic orbits (UPOs). It is shown that TDFC will drive a trajectory onto a periodic orbit while minimising an integral of a cost function of the error in ...
Barnett +9 more
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Reversible Relative Periodic Orbits [PDF]
Journal of Differential Equations, 2002 AbstractWe study the bundle structure near reversible relative periodic orbits in reversible equivariant systems. In particular we show that the vector field on the bundle forms a skew product system, by which the study of bifurcation from reversible relative periodic solutions reduces to the analysis of bifurcation from reversible discrete rotating ...
Lamb, JSW, Wulff, C
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On the distribution of periodic orbits
Discrete & Continuous Dynamical Systems - A, 2010 Let $f:M\to M$ be a $C^{1+ }$-map on a smooth Riemannian manifold $M$ and let $ \subset M$ be a compact $f$-invariant locally maximal set. In this paper we obtain several results concerning the distribution of the periodic orbits of $f| $. These results are non-invertible and, in particular, non-uniformly hyperbolic versions of well-known results by
Christian Wolf, Katrin Gelfert
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Measuring scars of periodic orbits [PDF]
Physical Review E, 1999 The phenomenon of periodic orbit scarring of eigenstates of classically chaotic systems is attracting increasing attention. Scarring is one of the most important "corrections" to the ideal random eigenstates suggested by random matrix theory. This paper discusses measures of scars and in so doing also tries to clarify the concepts and effects of ...
Lev Kaplan, Eric J. Heller
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Lyapunov-Schmidt Reduction for Unfolding Heteroclinic Networks of Equilibria and Periodic Orbits with Tangencies [PDF]
, 2010 This article concerns arbitrary finite heteroclinic networks in any phase space dimension whose vertices can be a random mixture of equilibria and periodic orbits. In addition, tangencies in the intersection of un/stable manifolds are allowed.
Rademacher, Jens D. M.
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Periodic-orbit theory of universal level correlations in quantum chaos [PDF]
, 2009 Using Gutzwiller's semiclassical periodic-orbit theory, we demonstrate universal behavior of the two-point correlator of the density of levels for quantum systems whose classical limit is fully chaotic. We go beyond previous work in establishing the full
S. Müller +4 more
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On the periodic orbits of Hamiltonian systems [PDF]
Journal of Mathematical Physics, 2010 We show how to apply to Hamiltonian differential systems recent results for studying the periodic orbits of a differential system using the averaging theory. We have chosen two classical integrable Hamiltonian systems, one with the Hooke potential and the other with the Kepler potential, and we study the periodic orbits which bifurcate from the ...
Llibre, Jaume, Rodrigues, Ana
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On the global dynamics of periodic triangular maps [PDF]
, 2016 This paper is an extension of an earlier paper that dealt with global dynamics in autonomous triangular maps. In the current paper, we extend the results on global dynamics of autonomous triangular maps to periodic non-autonomous triangular maps. We show
Luis, Rafael
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Periodic-orbit theory of universality in quantum chaos. [PDF]
Physical review. E, Statistical, nonlinear, and soft matter physics, 2005 We argue semiclassically, on the basis of Gutzwiller's periodic-orbit theory, that full classical chaos is paralleled by quantum energy spectra with universal spectral statistics, in agreement with random-matrix theory. For dynamics from all three Wigner-
S. Müller +4 more
semanticscholar +1 more source