Silverman J. — The arithmetic of dynamical systems :: Электронная библиотека попечительского совета мехмата МГУ

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Silverman J. — The arithmetic of dynamical systems

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Название: The arithmetic of dynamical systems

Автор: Silverman J.

Аннотация:

This book provides an introduction to the relatively new discipline of arithmetic dynamics. Whereas classical discrete dynamics is the study of iteration of self-maps of the complex plane or real line, arithmetic dynamics is the study of the number-theoretic properties of rational and algebraic points under repeated application of a polynomial or rational function. A principal theme of arithmetic dynamics is that many of the fundamental problems in the theory of Diophantine equations have dynamical analogs.This graduate-level text provides an entry for students into an active field of research and serves as a standard reference for researchers.

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Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 518

Добавлена в каталог: 08.02.2014

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Предметный указатель

Torsion point, of multiplicative group      326
Torsion subgroup      2
Torsion subgroup, elliptic curve, is equidistributed      127
Torsion subgroup, of elliptic curve      32 343 352
Torus      33
Totally disconnected      43 239
Totally disconnected, $\mathbb{C}_{p}$ is      239 276 294
Totally disconnected, Julia set      23 26
Totally ramified      12
Totally ramified, fixed point      16 37
Totient function      137 164 182
Totient function, iteration of      6
Tree, Berkovich disk is      298
Triangle inequality      44 87
Triangle inequality, nonarchimedean      44 70 242
Triangle inequality, ultrametric      44
Triangle inequality, uniform version      91
Trihomogeneous polynomial      437
Twist, associated 1-cocycle      201
Twist, cocycle corresponds to      203
Twist, elliptic curve      198
Twist, general theory      199
Twist, of $\mathbb{P}^{1}$       200
Twist, of $\mathbb{P}^{1}$ , trivial iff $C(K)\neq\emptyset$       215
Twist, of power map      206 328 380
Twist, of rational map      197 200
Twist, quadratic      198 200
Twist, same image in $\mathcal{M}_{d}$       198
Twist, set of injects into $H^{1}$       202 236
Twist, twist, $n^{th}$ root      204
Twist, twist, none if $Aut(\phi)$ is trivial      198
Twist, twist, of an object      199
Twist, twist, of Chebyshev polynomial      336
Twist, twist, of elliptic curve      341 374
Twist, with good reduction outside       237
Twisted action      211
Type — I point      295
Type — I point, as nested sequence of disks      322
Type — I point, attracting fixed point      324
Type — I point, attracting periodic      310
Type — I point, fixed point      322
Type — I point, intersection of orbit with open set      324
Type — I point, seminorm is not norm      297
Type — II point      295
Type — II point, as nested sequence of disks      322
Type — II point, fixed point      322
Type — II point, repelling periodic      310
Type — II point, seminorm is norm      297 321
Type — III point      295
Type — III point, as nested sequence of disks      322
Type — III point, fixed point      322
Type — III point, seminorm is norm      297 321
Type — IV point      295
Type — IV point, fixed point      322
Type — IV point, has positive radius      296 321
Type — IV point, is nested sequence of disks      295
Type — IV point, line segment to Gauss point      322
Type — IV point, no fixed in $\mathbb{A}^{\mathcal{B}}$       321
Type — IV point, seminorm is norm      297 321
Ullmo’s theorem      129
Ultrametric inequality      44 242
Ultrametric inequality, is an equality      45
Uncountable Julia set      267
Uncountable Julia set, Berkovich      307 311
Unicity conjecture for Markoff numbers      437
Uniform bound for integer points on elliptic curve      372
Uniform boundedness, for abelian varieties      97
Uniform boundedness, for elliptic curves      97 369
Uniform boundedness, for preperiodic points      96 135 368
Uniform boundedness, for preperiodic points, of $z^{d}$       137
Uniform boundedness, for preperiodic points, of Latt $\grave{e}$ s map      370
Uniform continuity      39 254 313
Uniform continuity, is open condition      254
Uniformization of Mandelbrot set      167 168

Uniformly Lipschitz      39 254 256 264 265 271
Uniformly Lipschitz, is open condition      254
Uniquely path connected      304
Uniqueness of height      408
Unirational variety      232
Unit group exact sequence      404
Unit, cyclotomic      69 72
Unit, dynamical      69 71 72 79 132 133
Unit, in dynatomic field      129
Universal cover      346
Unramified dynatomic field      131
Unramified field generated by torsion on elliptic curve      344 363
Unramified isogeny map is      340 353
Unsolved problem (**)      7
Valuation      44
Valuation, discrete      44
Valuation, normalized      44
Valued field      44
Valued field, complete      240
Valued field, completion      241
Valued field, disk      242
Valued field, extension of complete      241
Valued field, ultrametric inequality is an equality      45
Variety      2 89 147 159 376
Variety, divisor      403
Variety, double cover      410
Variety, involution      410
Variety, K3 surface      410
Variety, periodic      127
Variety, preperiodic      127 128
Variety, quotient      161 174
Variety, quotient by involution      410
Variety, rational      232
Variety, twist      200 211 236
Variety, unirational      232
Vector space associated to a divisor      406
Very ample divisor      406
Very highly ramified      231
Veselov’s theorem      431
Wandering disk component      283
Wandering disk domain      284 285
Wandering disk domain, exist over $\mathbb{C}_{p}$       285 286
Wandering domain      28
Wandering point      108
Wandering point, height lower bound      221
Wandering point, height of      432
Weak convergence of measures      128
Wehler’s theorem      418
Weierstrass $\wp$ function      34 345
Weierstrass class      223
Weierstrass class, trivial      223 237
Weierstrass equation      409
Weierstrass equation, elliptic curve      336
Weierstrass equation, generalized      336
Weierstrass equation, minimal      222
Weierstrass equation, Tate’s algorithm      342
Weierstrass preparation theorem      298
Weil height      see height
Weil height machine      89
Weil height machine, as map on Picard group      408
Weil height machine, effectivity of constants      408
Wildly critical point      37 284
Wildly critical point, most rational maps have no      284
Wildly critical recurrent points exist      285
Wreath product      125 164
Wreath product, dynatomic Galois group      125
Wreath product, of symmetric group and cyclic group      125
Yuan’s theorem      129
Zagier’s theorem      443
Zariski dense orbit      435
Zero of a meromorphic function      244
Zero of a rational function      403
Zero of holomorphic function are isolated      244
Zhang’s theorem      129

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