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Chaotic Dynamics papers — page 70

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Binary Tree Approach to Scaling in Unimodal Maps
Ge, Rusjan, and Zweifel (J. Stat. Phys. 59, 1265 (1990)) introduced a binary tree which represents all the periodic windows in the chaotic regime of iterated one-dimensional unimodal maps. We…
Jukka A. Ketoja, Juhani KurkijarviMay 6, 1993
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A Cayley Tree Immune Network Model with Antibody Dynamics
A Cayley tree model of idiotypic networks that includes both B cell and antibody dynamics is formulated and analyzed. As in models with B cells only, localized states exist in the network with…
Russell W. Anderson, Avidan U. Neumann, Alan S. PerelsonMay 3, 1993
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Twistless KAM tori, quasi flat homoclinic intersections, and other cancellations in the perturbation series of certain completely integrable hamiltonian systems. A review
Rotators interacting with a pendulum via small, velocity independent, potentials are considered. If the interaction potential does not depend on the pendulum position then the pendulum and the…
Giovanni GallavottiApr 29, 1993
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Explicit Lie-Poisson integration and the Euler equations
We give a wide class of Lie-Poisson systems for which explicit, Lie-Poisson integrators, preserving all Casimirs, can be constructed. The integrators are extremely simple. Examples are the rigid…
Robert I. McLachlanApr 28, 1993
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Dynamical Systems: Some Computational Problems
We present several topics involving the computation of dynamical systems. The emphasis is on work in progress and the presentation is informal -- there are many technical details which are not fully…
John Guckenheimer, Patrick WorfolkApr 27, 1993
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A Dynamical Simulation Facility for Hybrid Systems
This paper establishes a general framework for describing hybrid dynamical systems which is particularly suitable for numerical simulation. In this context, the data structures used to describe the…
Allen Back, John Guckenheimer, Mark MyersApr 21, 1993
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Braid analysis of (low-dimensional) chaos
Braid theory is used to calcualte the topological entropy of data from the belousov-Zhabotinskii reaction, the results agree well with one-dimensional theory to the order of approximation considered.
N. Tufillaro, CNLS, T-13 et al.Apr 20, 1993
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One-dimensional dynamics and factors of finite automata
We argue that simple dynamical systems are factors of finite automata, regarded as dynamical systems on discontinuum. We show that any homeomorphism of the real interval is of this class. An…
Petr KurkaApr 16, 1993
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Modifying the onset of homoclinic chaos. Application to a bistable potential
We analyze, by means of Melnikov method, the possibility of modifying the threshold of homoclinic chaos in general 1-dimensional problems, by introducing small periodic resonant modulations. We…
G. Cicogna, L. FronzoniApr 16, 1993
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Dissipation Induced Instabilities
The main goal of this paper is to prove that if the energy-momentum (or energy-Casimir) method predicts formal instability of a relative equilibrium in a Hamiltonian system with symmetry, then with…
Anthony Bloch, P. S. Krishnaprasad, Jerrold E. Marsden et al.Apr 14, 1993
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Inertial Forms of Navier-Stokes Equations on Sphere
The Navier--Stokes equations for incompressible flows past a two--dimensional sphere are considered in this article. The existence of an inertial form of the equations is established. Furthermore for…
Roger Temam, Shouhong WangApr 14, 1993
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A New Determinant for Quantum Chaos
We propose a new type of approximation to quantum determinants, ``quantum Fredholm determinant", and conjecture that, compared to the quantum Selberg zeta functions derived from Gutzwiller…
Predrag Cvitanović, Per E. RosenqvistApr 12, 1993
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Randomness in Arithmetic and The Decline and Fall of Reductionism in Pure Mathematics
Lecture given Thursday 22 October 1992 at a Mathematics-Computer Science Colloquium at the University of New Mexico. The lecture was videotaped; this is an edited transcript.
G. J. ChaitinApr 7, 1993
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Chaos in the one-dimensional gravitational three-body problem
We have investigated the appearance of chaos in the 1-dimensional Newtonian gravitational three-body system (three masses on a line with -1/r pairwise potential). We have concentrated in particular…
Jarmo Hietarinta, Seppo MikkolaApr 5, 1993
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The Escape Problem for Irreversible Systems
The problem of noise-induced escape from a metastable state arises in physics, chemistry, biology, systems engineering, and other areas. The problem is well understood when the underlying dynamics of…
Robert S. Maier, D. L. SteinMar 31, 1993
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Non-ergodicity for C1 Expanding Maps
In this paper, we consider the question of existence and uniqueness of absolutely continuous invariant measures for expanding C1 maps of the circle. This is a question which arises naturally from…
Anthony N. QuasMar 31, 1993
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Dynamical Systems Accepting the Normal Shift
Classical Bianchi-Lie, Backlund and Darboux transformations are considered. Their generalizations for the dynamical systems are discussed. For the transformation being the generalization of the…
A. Yu. Boldin, R. A. SharipovMar 28, 1993
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Symmetry Decomposition of Chaotic Dynamics
Discrete symmetries of dynamical flows give rise to relations between periodic orbits, reduce the dynamics to a fundamental domain, and lead to factorizations of zeta functions. These factorizations…
Predrag Cvitanović, Bruno EckhardtMar 24, 1993
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Dynamical Systems and Factors of Finite Automata
We conceive finite automata as dynamical systems on discontinuum and investigate their factors. Factors of finite automata include many well-known simple dynamical systems, e.g. hyperbolic systems…
Petr KurkaMar 23, 1993
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Periodic Orbit Theory
[[ RM: A review paper on cycle expansions. I quote the introduction: in section (2) ]] I will summarize Gutzwiller's theory for the spectrum of eigenenergies and extend it to diagonal matrix…
Bruno EckhardtMar 23, 1993
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Kramers map approach for stabilization of hydrogen atom in a magnetic field
The phenomenon of stabilization of highly excited states of hydrogen atom in a strong monochromatic field is discussed. Approximate description of dynamics by the introduced Kramers map allows to…
D. L. ShepelyanskyMar 23, 1993
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Field theory and KAM tori
The parametric equations of KAM tori for a quasi integrable system, are shown to be one point Schwinger functions of a suitable euclidean quantum field theory on the torus. KAM theorem is equivalent…
G. Gallavotti, G. Gentile, V. MastropietroMar 20, 1993
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Global Solutions of the Equations of Elastodynamics of Incompressible Neo-Hookean Materials
We prove that the initial-value problem for the motion of a certain type of elastic body has a solution for all time if the initial data are sufficiently small. The body must fill all of three space,…
David G. Ebin, SUNY at Stony Brook, NY 11794-3651Mar 18, 1993
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Order and chaos in quantum irregular scattering: Wigner's time delay
Recent developments in the semiclassical analysis of chaotic systems are reviewed and illustrated for Wigner's time delay in elastic scattering of a point particle from three disks in the plane.…
Bruno EckhardtMar 12, 1993
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Stochastic to deterministic crossover of fractal dimension for a Langevin equation
Using algorithms of Higuchi and of Grassberger and Procaccia, we study numerically how fractal dimensions cross over from finite-dimensional Brownian noise at short time scales to finite values of…
David A. Egolf, Henry S. GreensideMar 12, 1993
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