Quick search Find article
Quick search
Find article

About ergodicity in the family of limaçon billiards

Holger R Dullin1 and Arnd Bäcker2

Show affiliations


Recommended by T Prosen

By continuation from the hyperbolic limit of the cardioid billiard we show that there is an abundance of bifurcations in the family of limaçon billiards. The statistics of these bifurcation shows that the size of the stable intervals decreases with approximately the same rate as their number increases with the period. In particular, we give numerical evidence that arbitrarily close to the cardioid there are elliptic islands due to orbits created in saddle-node bifurcations. This shows explicitly that if in this one-parameter family of maps ergodicity occurs for more than one parameter, the set of these parameter values has a complicated structure.


PACS

05.45.Mt Quantum chaos; semiclassical methods

02.30.Oz Bifurcation theory

MSC

37Axx Ergodic theory (See also 28Dxx)

37G15 Bifurcations of limit cycles and periodic orbits

37E10 Maps of the circle

37D50 Hyperbolic systems with singularities (billiards, etc.)

Subjects

Mathematical physics

Statistical physics and nonlinear systems

Dates

Issue 6 (November 2001)

Received 4 April 2001

Published 22 October 2001



  1. About ergodicity in the family of limaçon billiards

    Holger R Dullin and Arnd Bäcker 2001 Nonlinearity 14 1673

  2. Generic twistless bifurcations

    H R Dullin et al 2000 Nonlinearity 13 203

  3. The baby Skyrme models and their multi-skyrmions

    Tom Weidig 1999 Nonlinearity 12 1489

  4. Computing connectedness: An exercise in computational topology

    V Robins et al 1998 Nonlinearity 11 913

  5. Generating partitions for two-dimensional hyperbolic maps

    A Bäcker and N Chernov 1998 Nonlinearity 11 79

  6. Quadratic volume-preserving maps

    Héctor E Lomelí and James D Meiss 1998 Nonlinearity 11 557

  7. How projections affect the dimension spectrum of fractal measures

    Brian R Hunt and Vadim Yu Kaloshin 1997 Nonlinearity 10 1031

  8. A silenced air pressure control valve

    P Bradshaw 1964 J. Sci. Instrum. 41 692

  9. Ultra-high vacuum system

    J A Turner et al 1962 J. Sci. Instrum. 39 26

  10. Apparatus for the rapid measurement of Seebeck coefficient

    M Fraser 1962 J. Sci. Instrum. 39 227

View by subject




Export








Please login to access our web services, or create an account if you don't yet have one.

You must have cookies enabled in your web browser to be able to login.

Username
Password

Forgotten your password? Get a new one here.