Entropy of Real Rational Surface Automorphisms
| Autor: | Jeffrey Diller, Kyounghee Kim |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Rational surface Entropy (statistical thermodynamics) General Mathematics 010102 general mathematics Dynamical Systems (math.DS) 0102 computer and information sciences Automorphism 01 natural sciences 37B40 37C05 37F10 Complex dynamics Quadratic equation 010201 computation theory & mathematics FOS: Mathematics Mathematics - Dynamical Systems 0101 mathematics Mathematics |
| Zdroj: | Experimental Mathematics. 30:172-190 |
| ISSN: | 1944-950X 1058-6458 |
| Popis: | We compare real and complex dynamics for automorphisms of rational surfaces that are obtained by lifting \chg{some} quadratic birational maps of the plane. In particular, we show how to exploit the existence of an invariant cubic curve to understand how the real part of an automorphism acts on homology. We apply this understanding to give examples where the entropy of the full (complex) automorphism is the same as its real restriction. Conversely and by different methods, we exhibit different examples where the entropy is strictly decreased by restricting to the real part of the surface. Finally, we give an example of a rational surface automorphism with positive entropy whose periodic cycles are all real. |
| Databáze: | OpenAIRE |
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