| Winter
semester |
|||
| Date |
Speaker |
Title |
Abstract |
| 8.10.2021 |
Presentation of the scope of the
seminar, fixing programme for the winter semester |
|
|
| 15.10.2021 |
Katarzyna
Sarosiek |
Iteration of
rational maps – examples |
|
| 22.10.2021 |
|||
| 29.10.2021 |
Joanna Horbaczewska | Properties of
the Julia set |
|
| 5.11.2021 |
|||
| 19.11.2021 |
Radosław Opoka |
Dynamics of a holomorhic map near
attracting/repelling fixed points |
|
| 26.11.2021 |
Radosław Opoka |
Dynamics of a holomorhic map near
superattracting and parabolic fixed points |
|
| 3.12.2021 |
Krzysztof Lech |
Dynamics of a holomorhic map near
irrationally neutral fixed points |
|
| 10.12.2021 |
Rafał Tryniecki |
Hausdorff dimension of sets with
restricted, slowly growing partial quotients |
I. J. Good (1941) showed that the set of
irrational numbers in $(0,1)$ whose partial quotients tend
to infinity is of Hausdorff dimension 1/2. A number of
related results impose restrictions of the type $a_n \in
B$ or $a_n \geq f(n)$, where $B$ is an infinite subset of
$\mathbb{N}$ and $f$ is a function rapidly growing with
$n$. We show that, for an arbitrary $B$ and an arbitrary
$f$ with values in $[\min B, \infty)$ and tending to
infinity, the set of irrational numbers in $(0, 1)$ such
that $a_n \in B$, $a_n \leq f(n)$ for all $n \in
\mathbb{N}$, and $a_n \to \infty$ as $n \to \infty$ is of
Hausdorff dimension $\tau(B)/2$, where $\tau(B)$ is the
exponent of convergence of $B$.
|
| 17.12.2021 |
Katarzyna Sarosiek |
Newton's method |
|
| 14.01.2022 |
Krzysztof Lech |
Dynamics of a holomorphic map mear an
irrationally neutral fixed point |
|
| 21.01.2022 |
Joanna Horbaczewska |
Dynamics of
transcendental maps from class $\mathcal B$ |
|
| 28.01.2022 | |||
| Summer
semester |
|||
| Date |
Speaker |
Title |
Abstract |
| 4.03.2022 |
Łukasz Pawelec |
Elements of infinite ergodic theory |
|
| 11.03.2022 |
Joanna Horbaczewska | Dimension and
measure of Julia sets of exponential maps |
|
| 18.03.2022 |
|
||
| 25.03.2022 |
Radosław Opoka | Indecomposable continua in exponential dynamics | |
| 1.04.2022 |
|||
| 8.04.2021 |
|||
| 22.04.2022 |
Rafał Tryniecki |
Hausdorff measure for continued fraction
expansions and piecewise-linear models |
|
| 29.04.2022 |
Krzysztof Lech |
Random holomorphic dynamics |
|
| 4.05.2022 |
Joanna Horbaczewska |
Indecomposable continua in exponential dynamics |
|
| 13.05.2022 |
Joanna Horbaczewska |
Indecomposable continua in exponential dynamics |
|
| 20.05.2021 |
Krzysztof Lech |
On iterates of $\exp(z)$ |
|
| 27.05.2022 |
Łukasz Pawelec |
Borel-Cantelli sequences in dynamics |
|
| 3.06.2022 |
Radosław Opoka |
Hairs of the complex exponential family |
|
| 10.06.2022 |
Summary of the seminar |
|
|