Piecewise Linear Models for the Quasiperiodic Transition to ChaosWe formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable…David K. Campbell, Roza Galeeva, Charles Tresser et al.·Feb 24, 1995SaveLearn
Strong Chaos without Butterfly Effect in Dynamical Systems with FeedbackWe discuss the predictability of a conservative system that drives a chaotic system with positive maximum Lyapunov exponent λ0, such as the erratic motion of an asteroid in the gravitational field…Guido Boffetta, Giovanni Paladin, Angelo Vulpiani·Feb 22, 1995SaveLearn
Two-dimensional Navier--Stokes simulation of deformation and break up of liquid patchesThe large deformations and break up of circular 2D liquid patches in a high Reynolds number (Re=1000) gas flow are investigated numerically. The 2D, plane flow Navier--Stokes equations are directly…S. Zaleski, Jie Li, S. Succi·Feb 21, 1995SaveLearn
Semiclassical Quantization of Billiards with Mixed Boundary ConditionsThe semiclassical theory for billiards with mixed boundary conditions is developed and explicit expressions for the smooth and the oscillatory parts of the spectral density are derived. The…Martin Sieber, Harel Primack, Uzy Smilansky et al.·Feb 19, 1995SaveLearn
How the viscous subrange determines inertial range properties in turbulence shell modelsWe calculate static solutions of the 'GOY' shell model of turbulence and do a linear stability analysis. The asymptotic limit of large Reynolds numbers is analyzed. A phase diagram is…Norbert Schörghofer, Leo Kadanoff, Detlef Lohse·Feb 15, 1995SaveLearn
Quantum manifestations of classical chaos in a Fermi accelerating diskWe study the classical and quantum mechanics of a free particle that collides elastically with the walls of a circular disk with the radius varying periodically in time. The quasi-energy spectral…R. Badrinarayanan, Jorge V. Jose, G. Chu·Feb 15, 1995SaveLearn
Complex Trkalian Fields and Solutions to Euler's Equations for the Ideal FluidWe consider solutions to the complex Trkalian equation,~ ∇ × = , where~ is a 3 component vector function with each component in the complex field, and may be expressed…P. R. Baldwin, G. M. Townsend·Feb 13, 1995SaveLearn
Coin Tossing as a Billiard ProblemWe demonstrate that the free motion of any two-dimensional rigid body colliding elastically with two parallel, flat walls is equivalent to a billiard system. Using this equivalence, we analyze the…N. L. Balazs, Rupak Chatterjee, A. D. Jackson·Feb 10, 1995SaveLearn
General Quantum Surface of Section MethodA new method for exact quantization of general bound Hamiltonian systems is presented. It is the quantum analogue of the classical Poincare Surface Of Section (SOS) reduction of classical dynamics.…Tomaz Prosen·Feb 8, 1995SaveLearn
Quantum Surface of Section Method: Decomposition of the Resolvent (E - H)(-1)The paper presents exact surface of section reduction of quantum mechanics. The main theoretical result is a decomposition of the energy-dependent propagator G(E) = (E - H)(-1) in terms of the…Tomaz Prosen·Feb 8, 1995SaveLearn
Quantum Surface of Section Method: Demonstration of semiclassical Berry-Robnik energy level spacing distribution in a generic 2-dim Hamiltonian systemThe recently developed quantum surface of section method is applied to a search for extremely high-lying energy levels in a simple but generic Hamiltonian system between integrability and chaos,…Tomaz Prosen·Feb 8, 1995SaveLearn
The ambiguous meaning of irreversibilityIrreversibility of spontaneous macroscopic dynamics and its asymmetry with respect to the sign reversal of the variable t is usually interpreted as a genuine property of complex isolated systems.…X. de Hemptinne·Feb 6, 1995SaveLearn
Bifurcations and Complete Chaos for the Diamagnetic Kepler ProblemWe describe the structure of bifurcations in the unbounded classical Diamagnetic Kepler problem. We conjecture that this system does not have any stable orbits and that the non-wandering set is…Kai T. Hansen·Feb 6, 1995SaveLearn
Symbolic Dynamics and Markov Partitions for the Stadium BilliardWe investigate the Bunimovich stadium dynamics and find that in the limit of infinitely long stadium the symbolic dynamics is a subshift of finite type. For a stadium of finite length the Markov…Kai T. Hansen, Predrag Cvitanovic·Feb 6, 1995SaveLearn
Inside-Outside Duality for Planar Billiards -- A Numerical StudyThis paper reports the results of extensive numerical studies related to spectral properties of the Laplacian and the scattering matrix for planar domains (called billiards). There is a close…Barbara Dietz, Jean-Pierre Eckmann, Claude-Alain Pillet et al.·Feb 5, 1995SaveLearn
Scattering Phases and Density of States for Exterior DomainFor a bounded open domain Ω∈ 2 with connected complement and piecewise smooth boundary, we consider the Dirichlet Laplacian - on Ω and the S-matrix on the complement Ωc. Using the…J. -P. Eckmann, C. -A. Pillet·Feb 4, 1995SaveLearn
Trace formulae for three-dimensional hyperbolic lattices and application to a strongly chaotic tetrahedral billiardThis paper is devoted to the quantum chaology of three-dimensional systems. A trace formula is derived for compact polyhedral billiards which tessellate the three-dimensional hyperbolic space of…R. Aurich, J. Marklof·Feb 3, 1995SaveLearn
Thermalization of a Brownian particle via coupling to low-dimensional chaosIt is shown that a paradigm of classical statistical mechanics --- the thermalization of a Brownian particle --- has a low-dimensional, deterministic analogue: when a heavy, slow system is coupled to…Christopher Jarzynski·Feb 2, 1995SaveLearn
Geometric phases and anholonomy for a class of chaotic classical systemsBerry's phase may be viewed as arising from the parallel transport of a quantal state around a loop in parameter space. In this Letter, the classical limit of this transport is obtained for a…Christopher Jarzynski·Feb 2, 1995SaveLearn
On the convergence of normalizing transformations in the presence of symmetriesIt is shown that, under suitable conditions, involving in particular the existence of analytic constants of motion, the presence of Lie point symmetries can ensure the convergence of the…G. Cicogna·Feb 2, 1995SaveLearn
Exact Resummations in the Theory of Hydrodynamic Turbulence: 0. Line-Resummed Diagrammatic Perturbation ApproachThe lectures presented by one of us (IP) at the Les Houches summer school dealt with the scaling properties of high Reynolds number turbulence in fluid flows. The results presented are available in…Victor L'vov, Itamar Procaccia·Feb 1, 1995SaveLearn
Quantization of the three dimensional Sinai billiardFor the first time a three--dimensional (3D) chaotic billiard -- the 3D Sinai billiard -- was quantized, and high--precision spectra with thousands of eigenvalues were calculated. We present here a…Harel Primack, Uzy Smilansky·Feb 1, 1995SaveLearn
Weyl Expansion for Symmetric PotentialsWe present a semiclassical expansion of the smooth part of the density of states in potentials with some form of symmetry. The density of states of each irreducible representation is separately…B. Lauritzen, N. D. Whelan·Feb 1, 1995SaveLearn
On the duality between periodic orbit statistics and quantum level statisticsWe discuss consequences of a recent observation that the sequence of periodic orbits in a chaotic billiard behaves like a poissonian stochastic process on small scales. This enables the semiclassical…Per Dahlqvist·Feb 1, 1995SaveLearn
SUPPLEMENT TO THE PAPER: Separating the regular and irregular energy levels and their statistics in Hamiltonian system with mixed classical dynamicsAs a technical supplement to the above mentioned paper we present 192 consecutive eigenstates for the Robnik billiard with the shape parameter λ=0.15 from 10,001st to 10,192nd, by showing the plots…Baowen Li, Marko Robnik·Feb 1, 1995SaveLearn