scholarly journals Surgery for partially hyperbolic dynamical systems II. Blow-up of a complex curve

2021 ◽  
Author(s):  
Andrey Gogolev ◽  
Federico Rodriguez Hertz
Keyword(s):  
Dynamical Systems ◽  
Blow Up ◽  
Complex Curve ◽  
Hyperbolic Dynamical Systems ◽  
Partially Hyperbolic

scholarly journals New partially hyperbolic dynamical systems I

2015 ◽  
Vol 215 (2) ◽  
pp. 363-393 ◽  
Author(s):  
Andrey Gogolev ◽  
Pedro Ontaneda ◽  
Federico Rodriguez Hertz
Keyword(s):  
Dynamical Systems ◽  
Hyperbolic Dynamical Systems ◽  
Partially Hyperbolic

scholarly journals Unstable entropy and unstable pressure for random partially hyperbolic dynamical systems

2020 ◽  
pp. 2150021
Author(s):  
Xinsheng Wang ◽  
Weisheng Wu ◽  
Yujun Zhu
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Variational Principle ◽  
Topological Entropy ◽  
Equilibrium States ◽  
Metric Entropy ◽  
Unstable Foliation ◽  
Hyperbolic Dynamical Systems ◽  
Partially Hyperbolic

Let [Formula: see text] be a [Formula: see text] random partially hyperbolic dynamical system. For the unstable foliation, the corresponding unstable metric entropy, unstable topological entropy and unstable pressure via the dynamics of [Formula: see text] on the unstable foliation are introduced and investigated. A version of Shannon–McMillan–Breiman Theorem for unstable metric entropy is given, and a variational principle for unstable pressure (and hence for unstable entropy) is obtained. Moreover, as an application of the variational principle, equilibrium states for the unstable pressure including Gibbs [Formula: see text]-states are investigated.

scholarly journals Local unstable entropy and local unstable pressure for random partially hyperbolic dynamical systems

2020 ◽  
Vol 40 (1) ◽  
pp. 81-105
Author(s):  
Xinsheng Wang ◽  
◽  
Weisheng Wu ◽  
Yujun Zhu ◽  
◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Hyperbolic Dynamical Systems ◽  
Partially Hyperbolic

scholarly journals Almost all $S$-integer dynamical systems have many periodic points

1998 ◽  
Vol 18 (2) ◽  
pp. 471-486 ◽  
Author(s):  
T. B. WARD
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Cellular Automata ◽  
Zeta Function ◽  
Periodic Points ◽  
Radius Of Convergence ◽  
Dynamical Zeta Function ◽  
Hyperbolic Dynamical Systems ◽  
Almost All

We show that for almost every ergodic $S$-integer dynamical system the radius of convergence of the dynamical zeta function is no larger than $\exp(-\frac{1}{2}h_{\rm top})<1$. In the arithmetic case almost every zeta function is irrational.We conjecture that for almost every ergodic $S$-integer dynamical system the radius of convergence of the zeta function is exactly $\exp(-h_{\rm top})<1$ and the zeta function is irrational.In an important geometric case (the $S$-integer systems corresponding to isometric extensions of the full $p$-shift or, more generally, linear algebraic cellular automata on the full $p$-shift) we show that the conjecture holds with the possible exception of at most two primes $p$.Finally, we explicitly describe the structure of $S$-integer dynamical systems as isometric extensions of (quasi-)hyperbolic dynamical systems.

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