# Homepage for Charlene Kalle

## Address

Mathematisch Instituut Universiteit Leiden Niels Bohrweg 1 2333 CA Leiden The Netherlands |
Room 212 Email: kallecccj@math.leidenuniv.nl Tel: +31 71 5271590 |

## Research

I'm an associate professor at Leiden University in the group of Frank den Hollander. Information about my former whereabouts can be found on my short CV.

### Keywords

interval maps, ergodic theory, dynamical systems, numeration systems, number expansions, fractal geometry

### PhD students

- Niels Langeveld: Matching, entropy, holes and expansions
- Marta Maggioni: Measures and matching for number systems
- Benthen Zeegers (started in November 2018)
- Jonny Imbierski (started in September 2020, joint with Dalia Terhesiu)

### Books

*A first course in ergodic theory*(with Karma Dajani), CRC Press, 2021.*Het gebruik van wiskunde in de Islam*(with Natasja Bouwman), Epsilon Uitgaven, Utrecht, 2002.

### Publications in international journals

*On approximation by random Lüroth expansions*(with Marta Maggioni). To appear in Int. J. Number Theory. (arXiv)*Invariant densities for random systems of the interval*(with Marta Maggioni). To appear in Ergodic Theory Dynam. Systems. (arXiv)*Matching for random systems with an application to minimal weight expansions*(with Karma Dajani and Marta Maggioni). Nonlinearity 34(6): 3676-3708, 2021. (arXiv)*The β-transformation with a hole at 0*(with Derong Kong, Niels Langeveld and Wenxia Li). Ergodic Theory Dynam. Systems 40(9): 2482-2514, 2020. (arXiv)*Invariant measures, matching and the frequency of 0 for signed binary expansions*(with Karma Dajani). Publ. Res. Inst. Math. Sci. 56(4): 701-742, 2020. (arXiv)*Matching for a family of infinite measure continued fraction transformations*(with Niels Langeveld, Marta Maggioni and Sara Munday). Discrete Contin. Dyn. Syst. 40(11): 6309-6330, 2020. (arXiv)*On the bifurcation set of unique expansions*(with Derong Kong, Wenxia Li and Fan Lü), Acta Arith. 188(4): 367-399, 2019. (arXiv)*The random continued fraction transformation*(with Tom Kempton and Evgeny Verbitskiy), Nonlinearity 30(3): 1182-1203, 2017. (arXiv)*Matching for generalised β-transformations*(with Henk Bruin and Carlo Carminati), Indag. Math. 28(1): 55-73, 2017. (arXiv)*Natural extensions for piecewise affine maps via Hofbauer towers*(with Henk Bruin), Monatsh. Math. 175(1): 65-88, 2014. (arXiv)*Isomorphisms between positive and negative beta-transformations*, Ergodic Theory Dynam. Systems 34(1): 153-170, 2014. (arXiv)*Local dimensions for the random β-transformation*(with Karma Dajani), New York J. Math. 19: 285-303, 2013. (arXiv)*Beta-expansions, natural extensions and multiple tilings*(with Wolfgang Steiner), Trans. Amer. Math. Soc. 364(5): 2281-2318, 2012. (arXiv)*Transformations generating negative β-expansions*(with Karma Dajani), Integers 11B, 2011, A5. (arXiv)*A note on the greedy β-transformation with arbitrary digits*(with Karma Dajani), in École de théorie ergodique, Sémin. Congr. 20, Soc. Math. France: 83-104, 2010. (PDF)*Natural extensions for the Golden Mean*(with Karma Dajani), in European Women in Mathematics, Proceedings of the 13th General Meeting, World Sci. Publ.: 113-123, 2010. (arXiv)*A natural extension for the greedy β-transformation with three arbitrary digits*(with Karma Dajani), Acta Math. Hungar. 125(1-2): 21--45, 2009. (PDF)*Random β-expansions with deleted digits*(with Karma Dajani), Discrete Contin. Dyn. Syst. 18(1): 199-217, 2007. (PDF)-
*On the convergence of logarithmic first return times*(with Karma Dajani), Rev. Roumaine Math. Pures Appl. 52(1): 35-46, 2007. (PDF)

### Publications in Dutch

*De oorsprong van ergodentheorie*(with Frank den Hollander), Nieuw Arch. Wiskd. (5), 22(1): 9-13, 2021. (PDF)*Tegeltjeswijsheden*, Eureka!, 49: 20-23, 2015. (PDF)*Bewogen getallen*, Nieuw Arch. Wiskd. (5), 12(1): 49-54, 2011. (PDF)

### Preprint

*Critical intermittency in random interval maps*(with Ale Jan Homburg, Marks Ruziboev, Evgeny Verbitskiy and Benthen Zeegers). (arXiv)

### Thesis

- Expansions and Extensions, 2009. (PDF)

## Workshops

Together with Carlo Carminati, Sara Munday and Evgeny Verbitskiy I organised the conference 60 years of dynamics and number expansions> from December 10 to 14, 2018 at the Centro Ennio de Giorgi in Pisa.

Together with Karma Dajani and Cor Kraaikamp I organised three one-day meetings in Ergodic Theory and Fractals in 2018. This was a sequal of a similar series of events that I organised with Tom Kempton in 2013.

From August 30 to September 2, 2016, there was a workshop on `Fractals, Ergodic Theory and Dynamical Systems' in Utrecht.

On the 11th and 12th of June 2015 there was a workshop on `Ergodic Theory and Dynamical Systems' in Leiden.

From the 20th to the 31st of Januari 2014 there was a school and workshop called Streams II at the Lorentz Center in Leiden.

## Teaching

In the fall semester of 2020-2021 I will be teaching the bachelor/master course Ergodic Theory and Fractals together with Evgeny Verbitskiy.

I will also be tutoring a group of first year mathematics students for the course Wiskundige Structuren.

In the spring semester of 2020-2021 I will be teaching Dynamics and Chaos for second year mathematics students together with Martina Chirilus-Bruckner.

## Studieadviseur

Sinds februari 2015 ben ik studieadviseur voor bachelorstudenten Wiskunde vanaf jaar 2. Klik hier voor informatie hierover.