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

Главная Ex Libris Книги Журналы Статьи Серии Каталог Wanted Загрузка ХудЛит Справка Поиск по индексам Поиск Форум

Авторизация

Поиск по указателям

Silverman J. — The arithmetic of dynamical systems

Обсудите книгу на научном форуме

Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter

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.

Язык:

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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Fixed point, Latt $\grave{e}$ s map      34
Fixed point, multiplier      18 47 180
Fixed point, multiplier, at infinity      38
Fixed point, neutral      322
Fixed point, no Type - IV      321
Fixed point, nonrepelling      255 314
Fixed point, nonrepelling, in Fatou set      256
Fixed point, of affine automorphism      427
Fixed point, of Chebyshev polynomial      332 380
Fixed point, of Chebyshev polynomial, in characteristic       381
Fixed point, of Type I, II, III, IV      322
Fixed point, rational      427
Fixed point, rational map      149
Fixed point, real      427
Fixed point, repelling in Julia set      256
Fixed point, residue index      38
Fixed point, rigid Latt $\grave{e}$ s map      366 384
Fixed point, summation formula      20 38 255 314 380 382
Fixed point, symmetric polynomial of multipliers      180
Fixed point, totally ramified      16 17 37
Flexible Latt $\acute{e}$ s map      187 355
Flexible Latt $\acute{e}$ s map, composition of      382
Flexible Latt $\acute{e}$ s map, degree      357
Flexible Latt $\acute{e}$ s map, fixed points      382 384
Flexible Latt $\acute{e}$ s map, good reduction      362 383
Flexible Latt $\acute{e}$ s map, multiplier      358 366 382 384
Flexible Latt $\acute{e}$ s map, multiplier at $\infty$       383
Flexible Latt $\acute{e}$ s map, multiplier, spectrum      356
Flexible Latt $\acute{e}$ s map, periodic points      358 382 384
FOD      see Field of definition
Foliated space      6
FOM      see Field of moduli
Formal derivative      12 37 313
Formal group      67
Formal multiplier spectrum      182 183
Formal multiplier spectrum, of $z^{2} + bz$       182
Formal multiplier spectrum, of $z^{d}$       182 183
Formal period      18 39 150
Formal period, $\nu_{d}{n)$ points of formal period       150 224
Formal period, algebraic family induces map to dynatomic curve      159
Formal period, algebraic family of points of given      159
Formal period, condition for smaller primitive period      151 165 226
Formal period, moduli problem      158
Formal power series      5
Formal power series, periodic points over ring of      78
Forward orbit      1 108 280 353
Fractional ideal      350
Fractional ideal, exact sequence      404
Fractional ideal, height formula      136
Fractional linear transformation respects reduction      50
Free product of cyclic groups      419 435
Frobenius map      351
Frobenius map, cyclotomic field      130
Frobenius map, periodic points are attracting      78
Function field      5
Function field, absolute values on      44
Function field, dynamics      5
Function, analytic      244
Function, equi - Lipschitz family      313
Function, equicontinuous family      254 264 265 271 306 313
Function, holomorphic      244
Function, meromorphic      244
Function, uniformly continuous family      39 254 313
Function, uniformly Lipschitz family      39 254 256 264 265 271 313 315
Functoriality of height      407 421
Fundamental domain      33 127
Galois cohomology      205
Galois conjugate, measure supported on      128
Galois equidistributed sequence      128
Galois equidistribution      128
Galois group, action on $PGL_{2}$       203
Galois group, action on dynatomic field      124
Galois group, action on projective space      122
Galois group, action on rational map      207 211
Galois group, cyclotomic field      129
Galois group, of dynatomic field      123 125
Galois group, of field generated by periodic points      122
Galois group, of fixed point      427
Galois group, orbit of conjugate point      137
Galois group, profinite topology      211
Galois group, subgroup associated to rational map      207
Galois group, subgroup of wreath product      125
Galois invariance of height      85
Galois theory      122
Galois-invariant orbit on K3 surface      436
Gauss norm      296
Gauss norm, associated Gauss point      297
Gauss norm, is sup norm      296
Gauss norm, on $\mathbb{C}_{p}[z]$       296
Gauss norm, on Tate algebra      298
Gauss point      297
Gauss point, fixed by polynomial      321
Gauss point, is Julia set of good reduction map      307 322
Gauss point, line segment to Type - IV point      322
Gauss point, of Berkovich disk of radius       301
Gel’fond metric      306
Gel’fond topology      300 322
Gel’fond topology, base of open sets      300
Gel’fond topology, not induced by path metric      306 323
Gel’fond topology, restricts to $\mathbb{C}_{p}$ topology      301 304 323
General linear group      10
Generalized dynatomic polynomial      227
Generalized dynatomic polynomial, for quadratic map      229
Generalized Weierstrass equation      336
Generating function for degree of rational map      397 428
Generic fiber      77
Generic rational map, dynamical unit      146
Generic rational map, not very highly ramified      231
Genus      15 37
Genus, of $X_{0}(n)$       164
Genus, of $X_{1}(4)$ , $X_{1}(5)$ , $X_{1}(6)$       230
Genus, of $X_{1}(n)$       164
Geometric invariant theory      176
Geometric point      337
Geometric quotient      179
Global -minimal model      237
Global minimal model      222
Global minimal model, implies trivial Weierstrass class      223
Global minimal model, over $\mathbb{Q}$       236
Global minimal Weierstrass equation      343 371
Global minimal Weierstrass equation, difference from quasiminimal      385
Good reduction      43 58 218
Good reduction, -adic distance between periodic points      69
Good reduction, abelian variety      442
Good reduction, attracting periodic points      64
Good reduction, Berkovich Julia set of map with      307 311 322
Good reduction, composition of maps      59 77
Good reduction, degree of reduction is same      58
Good reduction, elliptic curve      342 362 383
Good reduction, finiteness of periodic points      66
Good reduction, from bad reduction      218
Good reduction, Green function of map with      289 294 318
Good reduction, iff resultant is unit      58 218
Good reduction, implies reduction is homomorphism      342
Good reduction, is everywhere nonexpanding      59
Good reduction, Julia set is empty      59 239
Good reduction, local canonical height for      103 141
Good reduction, map on Berkovich disk      321 322
Good reduction, nonrepelling periodic points      64
Good reduction, of $\phi(P)$ is $\tilde{\phi}{\tilde{P})$       59
Good reduction, of a rational map      58
Good reduction, over power series ring of characteristic       78
Good reduction, period of reduced point      62 66 78
Good reduction, periodic points reduce to periodic points      61
Good reduction, potential      371
Good reduction, scheme-theoretic characterization      59 61 77
Good reduction, separable      64
Good reduction, twists with outside       237
Graph      150 216 226
Green function      287 288

Green function, algorithm to compute      318
Green function, complex      140
Green function, defining properties      289
Green function, homogeneity properties      289
Green function, is continuous      289
Green function, is H $\ddot{o}$ lder continuous      318
Green function, modified      318
Green function, of bad reduction map      294 318
Green function, of good reduction map      289 294 318
Green function, relation to local canonical height      291
Green function, sum is canonical height      290 318
Group      2
Group, action      234
Group, additive      30
Group, algebraic      325
Group, commutative algebraic      375
Group, dynamical system on      2
Group, law on elliptic curve      338
Group, multiplicative      29
Group, multiplicative scheme      29
Group, periodic points form subgroup      8
Group, variety $PGL_{2}$       170
Group, wreath product      125
H $\acute{e}$ non map      390 402
H $\acute{e}$ non map, number of orbits over a finite field      430
H $\acute{e}$ non map, reversible      430
H $\ddot{o}$ lder continuity of Green function      318
Haar measure      127
Half a loaf      133
Hard problem (textbf*)      7
Harmonic function, local canonical height is      140
Hausdorff space, Berkovich disk is      300
Hecke correspondence      369
Height      4 81
Height Machine      407
Height, $h([u,a,b])\leq h([u,a]) +h([u,b])$       398 428
Height, absolute      85
Height, absolute logarithmic      93
Height, additivity      408 421
Height, bounded for ample divisor is finite set      408
Height, canonical      97 99 100 287 409
Height, canonical, on K3 surface      421 426 435 436
Height, effect of morphism of degree d      90 136 398 407 409
Height, effect of rational map      388
Height, effectivity of constants      408
Height, elliptic curve      409
Height, elliptic curve, effect of multiplication map      409
Height, equals one iff root of unity      88 100
Height, field extension formula      84
Height, finitely many points of bounded      86 407 423
Height, for linearly equivalent divisors      408
Height, fractional ideal formula      136
Height, functoriality      407 421
Height, Galois invariance of      85
Height, in affine space      397
Height, inequality for jointly regular affine morphisms      397 429
Height, inequality for nonregular affine automorphism      429
Height, inequality for regular affine automorphisms      399 431
Height, infinitely many points of bounded      435
Height, is at least one      84
Height, is well-defined      84
Height, Lehmer’s conjecture      100 101 138
Height, logarithmic      93
Height, lower bound for      100 101 137 138 221
Height, machine      407
Height, map on Picard group      408
Height, Misiurewicz points have bounded      167
Height, number of points of bounded      135 136 441
Height, number of points of bounded, on K3 surface      425
Height, of a rational map      143
Height, of a rational point      82
Height, of an algebraic point      84
Height, of isolated periodic points is bounded      402
Height, of polynomial and its roots      136 138
Height, of wandering point for regular affine automorphism      432
Height, on $\mathbb{P}^{N}\times\mathbb{P}^{M}$       409 420
Height, on $\mthcal{M}_{d}$       237
Height, on K3 surface      420
Height, on projective space      407
Height, positivity      408
Height, product $\hat{h}^{+}\hat{h}^{-}$ of canonical      435
Height, transformation rules on K3 surface      420
Height, uniqueness      408
Height, Weil      89 407
Height, zeta function      436
Hensel’s Lemma      48
Herman ring      28
Hilbert basis theorem      90
Hilbert nullstellensatz      90 92
Hilbert theorem      90 199 205 207
Holomorphic function      244
Holomorphic function, coefficients uniquely determined      312
Holomorphic function, distance between image disks      268
Holomorphic function, dynamics of      23
Holomorphic function, equi - Lipschitz family      313
Holomorphic function, equicontinuous family      254 264 313
Holomorphic function, family omitting one point      264 315
Holomorphic function, Fatou set      24 255
Holomorphic function, is continuous      253
Holomorphic function, is open      253
Holomorphic function, Julia set      24 255
Holomorphic function, Lipschitz bound      248 254 272
Holomorphic function, maximum modulus principle      250
Holomorphic function, Montel theorem      264 271 315
Holomorphic function, Newton polygon      249
Holomorphic function, norm      247
Holomorphic function, norm of derivative      252 313
Holomorphic function, order of      244
Holomorphic function, product is holomorphic      312
Holomorphic function, reciprocal is holomorphic      313
Holomorphic function, roots determined by Newton polygon      249
Holomorphic function, sends disks to disks      252 305
Holomorphic function, uniformly continuous family      254 313
Holomorphic function, uniformly Lipschitz      254 264 265 271 313 315
Holomorphic function, zeros are isolated      244
Homogeneous coordinates      10
Homogeneous ideal      89
Homogeneous of degree $d^{n} + 1$       181
Homogeneous polynomial      10
Homogeneous polynomial, representation of integer by      105
Homogeneous seminorm      303 305
Homogeneous space      6
Homogenization      389
Hsia kernel      323
Hsia’s theorem      264 265 271 273
Hurwitz formula      13 217
Hyperbolic component of Mandelbrot set      166
Hyperbolic map      317
Hyperbolic map, nonarchimedean      279 285 317
Icosohedral group      197
Ideal class group      350
Ideal class group, exact sequence      404
Ideal class group, map to CM elliptic curves      350
Ideal, algebraic set attached to      90
Ideal, attached to an algebraic set      90
Ideal, Hilbert basis theorem      90
Ideal, homogeneous      89
Ideal, radical      89
Identity element of an elliptic curve      337
Imaginary field, quadratic      341
Immediate basin of attraction      310 311
In characteristic two      383
Inclusion- exclusion      148 224
Indeterminacy locus      389
Indeterminacy locus, dimension      394
Indeterminacy locus, disjoint      394
Indeterminacy locus, of involution on K3 surface      413
Indeterminacy locus, of iterate      394
Indifferent periodic point      19 326
Indifferent periodic point, one implies infinitely many      314

1 2 3 4 5 6 7 8 9 10 11

О проекте