Lamb, JSW

Melbourne, I

Wulff, C

Ergodic Theory and Dynamical Systems

English

Relative periodic solutions are ubiquitous in dynamical systems with continuous symmetry. Recently, Sandstede, Scheel and Wulff derived a center bundle theorem, reducing local bifurcation from relative periodic solutions to a finite-dimensional problem. Independently, Lamb and Melbourne showed how to systematically study local bifurcation from isolated periodic solutions with discrete spatiotemporal symmetries. In this paper, we show how the center bundle theorem, when combined with certain group theoretic results, reduces bifurcation from relative periodic solutions to bifurcation from isolated periodic solutions. In this way, we obtain a systematic approach to the study of local bifurcation from relative periodic solutions

Claudia Wulff

Jeroen S. W. Lamb

Ian Melbourne

CiteSeerX

Bifurcation from relative periodic solutions

Relative periodic solutions are ubiquitous in dynamical systems with continuous symmetry. Recently, Sandstede, Scheel and Wulff derived a center bundle theorem, reducing local bifurcation from relative periodic solutions to a finite-dimensional problem. Independently, Lamb and Melbourne showed how to systematically study local bifurcation from isolated periodic solutions with discrete spatiotemporal symmetries.


In this paper, we show how the center bundle theorem, when combined with certain group theoretic results, reduces bifurcation from relative periodic solutions to bifurcation
from isolated periodic solutions. In this way, we obtain a systematic approach to the study of local bifurcation from relative periodic solutions.</p

Wulff, Claudia

Lamb, Jeroen S. W.

Melbourne, Ian

Surrey Research Insight

Spiral - Imperial College Digital Repository

Bifurcation from discrete rotating waves.

Bifurcation from periodic solutions with spatiotemporal symmetry.

Bifurcation from relative equilibria to non-compact group actions: Skew products, meanders, and drifts.

Bifurcations and dynamics of spiral waves.

Bifurcations of periodic orbits with spatio-temporal symmetries.

Bifurcations of relative equilibria.

Compact Lie Groups and their Representations (Transl.

Cycloidal circulation of spiral waves in an excitable medium.

Dynamics of spiral waves on unbounded domains using centermanifold reductions.

Equivariant dynamical systems.

Equivariant period doubling. Advanced Topics in the Theory of Dynamical Systems (Notes Rep.

Flow regimes in a circular Couette system with independently rotating cylinders.

General bifurcations from periodic solutions with spatiotemporal symmetry, including mode interactions and resonances, in preparation.

Hopf bifurcation from rotating waves and patterns in physical space.

Index of the exponential map of a semialgebraic group.

Iterates of maps with symmetry.

Local structure for equivariant dynamics. Singularity Theory and its Applications, Part II

Noncompact drift for relative equilibria and relative periodic orbits.

Nonlinear Oscillations, Dynamical Systems,

Normal forms, resonances, and meandering tip motions near relative equilibria of Euclidean group actions.

On the existence of slices for actions of non-compact Lie groups.

On the interaction of vortices in two-dimensional active media.

Period-doublings and orbit-bifurcations in symmetric systems.

Periodic to quasiperiodic transition of chemical spiral rotation.

Reversing k-symmetries in dynamical systems.

Rotating and modulated rotating states of cellular ﬂames.

Some remarks on period doubling in systems with symmetry.

Some theorems on matrices with real quaternionic elements.

Spatial and temporal characteristics of modulated waves in the circular Couette system.

Symmetries in modulated traveling waves in combustion: jumping ponies on a merry-go-round. Pattern Formation:

Symmetry breaking for equivariant maps. Algebraic Groups and Related Subjects (Australian

Transition from simple rotating chemical spirals to meandering and traveling spirals.

Walter de Gruyter,

Relative periodic solutions are ubiquitous in dynamical systems with continuous symmetry. Recently, Sandstede, Scheel and Wulff derived a center bundle theorem, reducing local bifurcation from relative periodic solutions to a finite-dimensional problem. Independently, Lamb and Melbourne showed how to systematically study local bifurcation from isolated periodic solutions with discrete spatiotemporal symmetries.In this paper, we show how the center bundle theorem, when combined with certain group theoretic results, reduces bifurcation from relative periodic solutions to bifurcation from isolated periodic solutions. In this way, we obtain a systematic approach to the study of local bifurcation from relative periodic solutions.</jats:p

Bifurcation from relative periodic solutions

Abstract

Similar works

Full text

Available Versions

CiteSeerX

Surrey Research Insight

Spiral - Imperial College Digital Repository

Crossref