Counting periodic points on quotient varieties over Fq

2018 ◽  
Vol 192 ◽  
pp. 386-405 ◽  
Author(s):  
Laura Walton
Keyword(s):  
Periodic Points ◽  
Quotient Varieties

Rational Periodic Points of the Quadratic Function Q c (x) = x 2 + c

1994 ◽  
Vol 101 (4) ◽  
pp. 318 ◽  
Author(s):  
Ralph Walde ◽  
Paula Russo
Keyword(s):  
Quadratic Function ◽  
Periodic Points

scholarly journals A topological lens for a measure-preserving system

2010 ◽  
Vol 31 (1) ◽  
pp. 49-75 ◽  
Author(s):  
E. GLASNER ◽  
M. LEMAŃCZYK ◽  
B. WEISS
Keyword(s):  
Topological Entropy ◽  
Periodic Points ◽  
Positive Entropy ◽  
Topological Properties ◽  
Topologically Transitive ◽  
Topological System ◽  
Zero Entropy ◽  
Weakly Mixing ◽  
Dynamical Properties

AbstractWe introduce a functor which associates to every measure-preserving system (X,ℬ,μ,T) a topological system $(C_2(\mu ),\tilde {T})$ defined on the space of twofold couplings of μ, called the topological lens of T. We show that often the topological lens ‘magnifies’ the basic measure dynamical properties of T in terms of the corresponding topological properties of $\tilde {T}$. Some of our main results are as follows: (i) T is weakly mixing if and only if $\tilde {T}$ is topologically transitive (if and only if it is topologically weakly mixing); (ii) T has zero entropy if and only if $\tilde {T}$ has zero topological entropy, and T has positive entropy if and only if $\tilde {T}$ has infinite topological entropy; (iii) for T a K-system, the topological lens is a P-system (i.e. it is topologically transitive and the set of periodic points is dense; such systems are also called chaotic in the sense of Devaney).

"CROSSROAD AREA–SPRING AREA" TRANSITION (II) FOLIATED PARAMETRIC REPRESENTATION

1991 ◽  
Vol 01 (02) ◽  
pp. 339-348 ◽  
Author(s):  
C. MIRA ◽  
J. P. CARCASSÈS ◽  
M. BOSCH ◽  
C. SIMÓ ◽  
J. C. TATJER
Keyword(s):  
Complete Information ◽  
Parametric Representation ◽  
Periodic Points ◽  
Parameter Plane ◽  
Flip Bifurcation ◽  
Cusp Point ◽  
Dimensional Representation ◽  
Bifurcation Structure ◽  
Spring Area

The areas considered are related to two different configurations of fold and flip bifurcation curves of maps, centred at a cusp point of a fold curve. This paper is a continuation of an earlier one devoted to parameter plane representation. Now the transition is studied in a thee-dimensional representation by introducing a norm associated with fixed or periodic points. This gives rise to complete information on the map bifurcation structure.

RATIONALITY OF SOME QUOTIENT VARIETIES

1986 ◽  
Vol 54 (2) ◽  
pp. 571-576 ◽  
Author(s):  
F A Bogomolov ◽  
P I Katsylo
Keyword(s):  
Quotient Varieties

SIMPLE AND COMPLEX DYNAMICS FOR ONE-DIMENSIONAL MANIFOLD MAPS

1995 ◽  
Vol 05 (05) ◽  
pp. 1351-1355
Author(s):  
VLADIMIR FEDORENKO
Keyword(s):  
Topological Entropy ◽  
Complex Dynamics ◽  
Periodic Points ◽  
Dimensional Manifold ◽  
One Dimensional ◽  
Circle Maps ◽  
Interval Maps ◽  
Chain Recurrent Set ◽  
Recurrent Set

We give a characterization of complex and simple interval maps and circle maps (in the sense of positive or zero topological entropy respectively), formulated in terms of the description of the dynamics of the map on its chain recurrent set. We also describe the behavior of complex maps on their periodic points.

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.

scholarly journals On orbits of endomorphisms of tori and the Schmidt game

1988 ◽  
Vol 8 (4) ◽  
pp. 523-529 ◽  
Author(s):  
S. G. Dani
Keyword(s):  
Hausdorff Dimension ◽  
Periodic Points ◽  
Dimensional Torus

AbstractWe show that there exists a subset F of the n-dimensional torus n such that F has Hausdorff dimension n and for any x∈F and any semisimple automorphism σ of n the closure of the σ-orbit of x contains no periodic points.

scholarly journals Generalizations of the Poincaré Birkhoff fixed point theorem

1977 ◽  
Vol 17 (3) ◽  
pp. 375-389 ◽  
Author(s):  
Walter D. Neumann
Keyword(s):  
Fixed Point ◽  
Lower Bound ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Periodic Points ◽  
Open Problems ◽  
Number Of Components ◽  
Birkhoff Theorem

It is shown how George D. Birkhoff's proof of the Poincaré Birkhoff theorem can be modified using ideas of H. Poincaré to give a rather precise lower bound on the number of components of the set of periodic points of the annulus. Some open problems related to this theorem are discussed.

scholarly journals Towards a classification of rigid product quotient varieties of Kodaira dimension 0

2021 ◽  
Author(s):  
Ingrid Bauer ◽  
Christian Gleissner
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Structure Theorem ◽  
Complete Classification ◽  
Kodaira Dimension ◽  
The Other ◽  
Diagonal Action ◽  
Quotient Varieties ◽  
A Finite Group

AbstractIn this paper the authors study quotients of the product of elliptic curves by a rigid diagonal action of a finite group G. It is shown that only for $$G = {{\,\mathrm{He}\,}}(3), {\mathbb {Z}}_3^2$$ G = He ( 3 ) , Z 3 2 , and only for dimension $$\ge 4$$ ≥ 4 such an action can be free. A complete classification of the singular quotients in dimension 3 and the smooth quotients in dimension 4 is given. For the other finite groups a strong structure theorem for rigid quotients is proven.

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