Dr Stefanie Hittmeyer

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Research Fellow

Biography

I am a Research Fellow in Applied Mathematics at the University of Auckland, specialising in dynamical systems, chaos and bifurcation theory. My research focuses on a higher-dimensional type of chaos called “wild chaos”. My research aims to find the geometric mechanisms that generate this abstract type of chaos in explicit systems. Moreover, I study how this type of chaos can be identified in applications by developing advanced numerical methods for the computation of invariant sets (such as stable and unstable manifolds) and the identification and continuation of their bifurcations. This type of dynamics can appear in noninvertible maps of dimension at least two, diffeomorphisms of dimension at least three and vector fields of dimension at least four.

After finishing my Diploma degree in Mathematics at Bielefeld University (Germany) in 2009, I started my PhD at the University of Bristol (UK) with Hinke Osinga and Bernd Krauskopf in 2010. Together with my supervisors I transferred to the University of Auckland in 2011, where I completed my PhD thesis in 2013.

Please visit my homepage for more detailed information.

Research | Current

  • Higher-dimensional chaos: wild chaos, heterodimensional cycles, blenders
  • Lorenz-like systems and their invariant manifolds
  • Bifurcations of noninvertible maps
  • Generalised Julia and Mandelbrot sets in nonanalytic maps
  • The Allee effect in predator-prey dynamics

Teaching | Current

I have been a lecturer for the courses

  • Differential Equations (Maths260)
  • Great Ideas Shaping our World (Maths190)
  • Numerical Computation (Maths270)

Distinctions/Honours

My name was put on the Graduate Dean’s list of excellent doctoral theses and I was suggested for the Vice Chancellors Best Thesis Award in 2014. Furthermore my PhD research was recognised by the Aitken Prize for the best student talk at the New Zealand Mathematical Society Colloquium 2012.

Areas of expertise

  • chaos
  • dynamical systems
  • bifurcations
  • invariant manifolds

Selected publications and creative works (Research Outputs)

  • Hittmeyer, S., Krauskopf, B., Osinga, H. M., & Shinohara, K. (2018). Existence of blenders in a Henon-like family: geometric insights from invariant manifold computations. NONLINEARITY, 31 (10), R239-R267. 10.1088/1361-6544/aacd66
    Other University of Auckland co-authors: Bernd Krauskopf, Hinke Osinga
  • Hittmeyer, S., Krauskopf, B., & Osinga, H. M. (2015). From wild Lorenz-like to wild Rovella-like dynamics. Dynamical Systems, 30 (4), 525-542. 10.1080/14689367.2015.1081677
    Other University of Auckland co-authors: Bernd Krauskopf, Hinke Osinga
  • Hittmeyer, S., Krauskopf, B., & Osinga, H. M. (2015). Interactions of the Julia set with critical and (un)stable sets in an angle-doubling map on C\{0}. International Journal of Bifurcation and Chaos, 25 (4)10.1142/S021812741530013X
    Other University of Auckland co-authors: Bernd Krauskopf, Hinke Osinga
  • Hittmeyer, S., Krauskopf, B., & Osinga, H. M. (2014). Bifurcations of generalised Julia sets near the complex quadratic family. Paper presented at International Congress of Women Mathematicians (ICWM) 2014, Seoul, Korea. 12 August - 14 August 2014. Proceedings of the International Congress of Women Mathematicians (ICWM) 2014.
    Other University of Auckland co-authors: Bernd Krauskopf, Hinke Osinga
  • Hittmeyer, S. (2014). Bifurcations of invariant sets in a model of wild chaos The University of Auckland. ResearchSpace@Auckland. Related URL.
    URL: http://hdl.handle.net/2292/22035

Identifiers

Contact details

Office hours

by appointment

Primary office location

SCIENCE CENTRE 303 - Bldg 303
Level 2, Room 222
38 PRINCES ST
AUCKLAND CENTRAL
AUCKLAND 1010
New Zealand

Web links