Text only print
Full screen print
Seminar on Geometric Complex Analysis
Seminar information archive ～10/15｜Next seminar｜Future seminars 10/16～
| Date, time & place | Monday 10:30 - 12:00 128Room #128 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Kengo Hirachi, Shigeharu Takayama |
2018/04/23
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yûsuke Okuyama (Kyoto Institute of Technology)
Degeneration and bifurcation of quadratic endomorphisms of $\mathbb{P}^2$ towards a Hénon map (JAPANESE)
Yûsuke Okuyama (Kyoto Institute of Technology)
Degeneration and bifurcation of quadratic endomorphisms of $\mathbb{P}^2$ towards a Hénon map (JAPANESE)
[ Abstract ]
The space of quadratic holomorphic endomorphisms of P^2 (over C) is
canonically identified with the complement of the zero locus of the
resultant form on P^{17}, and all H¥'enon maps, which are (the only)
interesting ones among all the quadratic polynomial automorphisms of C^2,
live in this zero locus.
We will talk about our joint work with Fabrizio Bianchi (Imperial College,
London) on the (algebraic) degeneration of quadratic endomorphisms of C^2
towards H¥'enon maps in terms of Berteloot-Bianchi-Dupont's
bifurcation/unstability theory of holomorphic families of endomorphisms of P^k,
which mostly generalizes Ma¥~n¥'e-Sad-Sullivan, Lyubich, and DeMarco's seminal
and similar theory on P^1.
Some preliminary knowledge on ergodic theory and pluripotential theory
would be desirable, but not be assumed.
The space of quadratic holomorphic endomorphisms of P^2 (over C) is
canonically identified with the complement of the zero locus of the
resultant form on P^{17}, and all H¥'enon maps, which are (the only)
interesting ones among all the quadratic polynomial automorphisms of C^2,
live in this zero locus.
We will talk about our joint work with Fabrizio Bianchi (Imperial College,
London) on the (algebraic) degeneration of quadratic endomorphisms of C^2
towards H¥'enon maps in terms of Berteloot-Bianchi-Dupont's
bifurcation/unstability theory of holomorphic families of endomorphisms of P^k,
which mostly generalizes Ma¥~n¥'e-Sad-Sullivan, Lyubich, and DeMarco's seminal
and similar theory on P^1.
Some preliminary knowledge on ergodic theory and pluripotential theory
would be desirable, but not be assumed.
