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  5. Dynamical Systems

Dynamical Systems

Colourful factal image

The interests of the Dynamical Systems Research Group include:

  • Applied analysis: renormalization theory and nonlinear dynamical systems
  • Complex analysis: the boundary behaviour of analytic and subharmonic functions
  • Complex dynamics: the structure of the escaping set and dimensions of Julia sets of transcendental entire functions
  • Fractal geometry: the structure of sets and measures in Euclidean spaces
  • Hyperbolic geometry and continued fraction theory
  • Value distribution and quasiregular mappings

Professor Gwyneth Stallard and Professor Phil Rippon have both been awarded the London Mathematical Society Whitehead Prize. Their research is currently funded by two EPSRC grants, entitled Baker's conjecture and Eremenko's conjecture: new directions and Dimensions in complex dynamics: spiders' webs and speed of escape

Aperiodic Order

Aperiodic Order is concerned with the investigation of discrete structures in space, such as point sets or tilings, which possess a certain degree of order while not showing any translational symmetry. A mathematical introduction to the field is provided by the book Aperiodic Order, recently published by Cambridge University Press.

Dynamical Systems Theory

Dynamical systems (often loosely referred to as "chaos theory") is the study of the solutions of nonlinear differential equations (or of maps in the case of discrete-time systems). Research in applied nonlinear dynamical systems includes the study of the transition to chaos, which often has remarkable properties that are "universal", i.e. common to a large class of models.