One-sided Lebesgue Bernoulli maps of the sphere of degree and .
Barnes, Julia A., Koss, Lorelei (2000)
International Journal of Mathematics and Mathematical Sciences
Pastor, G., Romera, M., Alvarez, G., Nunez, J., Arroyo, D., Montoya, F. (2007)
Discrete Dynamics in Nature and Society
Anna Zdunik (1990)
Inventiones mathematicae
Artur Avila, Mikhail Lyubich, Weixiao Shen (2011)
Journal of the European Mathematical Society
We study the parameter space of unicritical polynomials . For complex parameters, we prove that for Lebesgue almost every , the map is either hyperbolic or infinitely renormalizable. For real parameters, we prove that for Lebesgue almost every , the map is either hyperbolic, or Collet–Eckmann, or infinitely renormalizable. These results are based on controlling the spacing between consecutive elements in the “principal nest” of parapuzzle pieces.
Milnor, John (2004)
Experimental Mathematics
Schleicher, Dierk, Zimmer, Johannes (2003)
Annales Academiae Scientiarum Fennicae. Mathematica
Romanovski, Valery G. (2007)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
Eric Bedford, John Smillie (1999)
Annales scientifiques de l'École Normale Supérieure
Eric Bedford, John Smillie (1991)
Inventiones mathematicae
Eric Bedford, John Smillie (1992)
Mathematische Annalen
Eric Bedford, M. Lyubich, John Smilie (1993)
Inventiones mathematicae
Scott Crass (2002)
Visual Mathematics
Przytycki, F., Urbański, M. (2001)
Annales Academiae Scientiarum Fennicae. Mathematica
Yan Gao (2016)
Fundamenta Mathematicae
The preperiodic dynatomic curve is the closure in ℂ² of the set of (c,z) such that z is a preperiodic point of the polynomial with preperiod n and period p (n,p ≥ 1). We prove that each has exactly d-1 irreducible components, which are all smooth and have pairwise transverse intersections at the singular points of . We also compute the genus of each component and the Galois group of the defining polynomial of .
Tomova, Anna (2001)
International Journal of Mathematics and Mathematical Sciences
Jan Kiwi (2006)
Annales de l’institut Fourier
We let be the completion of the field of formal Puiseux series and study polynomials with coefficients in as dynamical systems. We give a complete description of the dynamical and parameter space of cubic polynomials in . We show that cubic polynomial dynamics over and are intimately related. More precisely, we establish that some elements of naturally correspond to the Fourier series of analytic almost periodic functions (in the sense of Bohr) which parametrize (near infinity) the quasiconformal...
Jan-Li Lin (2012)
Bulletin de la Société Mathématique de France
We study the pullback maps on cohomology groups for equivariant rational maps (i.e., monomial maps) on toric varieties. Our method is based on the intersection theory on toric varieties. We use the method to determine the dynamical degrees of monomial maps and compute the degrees of the Cremona involution.
Bracci Filippo (2001)
Bollettino dell'Unione Matematica Italiana
Magnus Aspenberg (2009)
Fundamenta Mathematicae
We show that Misiurewicz maps for which the Julia set is not the whole sphere are Lebesgue density points of hyperbolic maps.
Benjamin Hutz (2010)
Acta Arithmetica