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Silverman J. — The arithmetic of dynamical systems
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.



Язык: en

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
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Предметный указатель
Primitive periodic point, dynatomic field      123
Primitive periodic point, field generated by      123
Primitive periodic point, set of is Galois-invariant      123
Principal divisor      320 339
Principal divisor, has degree zero      339
Probability measure      127
Probability measure, Borel      127
Probability measure, canonical      127
Probability measure, canonical on Berkovich space      306
Probability measure, invariant      127
Product formula      83 84 290
Profinite topology      211
Projection map      287
Projection map, of K3 surface to $\mathbb{P}^{2}$      410
Projective general linear group      10
Projective line, automorphism group      10
Projective line, Berkovich      302
Projective line, change of variables      11
Projective line, chordal metric      11 35
Projective line, construction of      10
Projective line, integer points on      106 108
Projective line, inversion is isometry      35
Projective line, linear fractional transformation      10
Projective line, morphism of over a variety      171
Projective line, moving three points      10 36 51
Projective line, not locally compact over $\mathbb{C}_{p}$      294
Projective line, over a variety      171
Projective line, point at infinity      10 11
Projective line, rational map      10
Projective line, Riemann sphere      10
Projective line, Riemann — Hurwitz formula      13 217
Projective line, spherical measure      36
Projective line, twist      200
Projective line, twist trivial iff $C(K)\neq 0$      215
Projective line, universal map of degree d      171
Projective space, absolute value of a point      90
Projective space, action of Galois group      122
Projective space, compact iff $K$ locally compact      243
Projective space, cross-ratio      71 79 132 348
Projective space, degree map on divisors      405
Projective space, field of definition of point      86 122
Projective space, finitely many points of bounded projective space, height      86
Projective space, height      82 84 407
Projective space, hyperplane generates Picard group      405
Projective space, monomial map      428
Projective space, morphism      89 388
Projective space, morphism, is open map      433
Projective space, moving $N + 2$ points      75
Projective space, nondegenerate automorphism      226
Projective space, normalized coordinates      49
Projective space, number of points of bounded height      135 136
Projective space, probability measure      127
Projective space, product of two      405
Projective space, product of two, K3 surface in      410
Projective space, product of two, surface with involutions in      436
Projective space, projection map to      287
Projective space, rational map      89 388
Projective space, Segre embedding      406
Projective special linear group      see PSL
PSL      175
PSL, map to PGL      175 231
PSL, stable locus      176
Puiseux series      5
Pullback divisor      404
Pullback divisor, linearly equivalent      405
Pushforward divisor      404
QRT family of integrable maps      443
Quadratic formula      261
Quadratic imaginary field      341
Quadratic imaginary field, class number      350 368
Quadratic imaginary field, fractional ideals in      350
Quadratic imaginary field, ideal class group      350
Quadratic map, algebraic family of      159 194 230
Quadratic map, algebraic family, induces map to dynatomic curve      159
Quadratic map, associated multiplier polynomial      227
Quadratic map, automorphism group contains $\mu_{2}$      235
Quadratic map, automorphism of order two      96 235
Quadratic map, bifurcation point      165
Quadratic map, bound for periodic points      96
Quadratic map, canonical height      137 138
Quadratic map, conjugation to $z^{2} + c$      156
Quadratic map, degenerate      194
Quadratic map, dynamical unit      134 145 146
Quadratic map, dynatomic curve      156 157
Quadratic map, dynatomic field      123
Quadratic map, dynatomic field, ramification      131
Quadratic map, dynatomic polynomial      39
Quadratic map, explicit formula for $\sigma_{1} (\phi)$      181
Quadratic map, generalized dynatomic polynomial      229
Quadratic map, local canonical height      141
Quadratic map, Mandelbrot set      26 165
Quadratic map, Misiurewicz point      166
Quadratic map, Misiurewicz point, minimal polynomial      230
Quadratic map, orbit of critical point      26 165
Quadratic map, parameter space has dimension three      168
Quadratic map, polynomial iff $\sigma_{1} (\phi) = 2$      232
Quadratic map, rational periodic points      137
Quadratic map, reducible dynatomic polynomial      235
Quadratic map, space of conjugacy classes has dimension one      168
Quadratic map, with preperiodic critical point      166
Quadratic twist      198
Quadratic twist, rational map      200
Quasiminimal Weierstrass equation      371
Quasiminimal Weierstrass equation, difference from global minimal      385
Quaternion algebra      341 378
Quotient curve      161
Quotient curve, critical values      353
Quotient curve, dynatomic      161
Quotient curve, elliptic      346
Quotient variety      410
Quotient variety, $Rat_{d}$ modulo $PSL_{2}$      175
Quotient variety, by finite group      161
Quotient variety, by infinite group      161 174
Quotient variety, categorical      179
Quotient variety, field of definition      161
Quotient variety, geometric      179
Quotient variety, rational points on      177
Quotient variety, semistable      179
Quotient variety, stable      179
Radical of an ideal      89
Radius of Berkovich disk      297 301
Radius of Berkovich point      296
Radius of Type-lV point is positive      296
Ramification index      12 36 340
Ramification index, automorphism invariant      234
Ramification index, divisibility by $p$      37
Ramification index, effect on chordal metric      115 144
Ramification index, large implies preperiodic      37
Ramification index, of iterate      117
Ramification index, of Latt$\grave{e}$s projection      384
Ramification index, sum of over inverse image of a point      15
Ramification point      see critical point
Ramification, field generated by torsion on elliptic curve      363
Ramification, in dynatomic field      129 131
Ramification, in field generated by torsion on elliptic curve      344
Rational automorphism      430
Rational function      9
Rational function, divisor      320
Rational function, finitely many nonzero residues      314
Rational function, formal derivative      12 313
Rational function, induces rational map      10
Rational function, integer values of      106
Rational function, maximum modulus principle      250
Rational function, pole      403
Rational function, principal divisor      320
Rational function, residue      313
Rational function, Schwarzian derivative      231
Rational function, space of associated to a divisor      406
Rational function, Taylor series      12
Rational function, zero      403
Rational map      10 89 388
Rational map, $az + b/z$      96 235
Rational map, $n$-period polynomial      181
Rational map, $PGL_{2}$-equivalence      195 233
Rational map, $PGL_{2}(K)$-equivalence      195 233
Rational map, $S$-integer points in orbit      143
Rational map, $z + b/z$      197 198
Rational map, $\acute{e}$tale      353
Rational map, action of automorphism on critical point      234
Rational map, action of Galois      207 211
Rational map, acts on $X_{1}(n)$      161
Rational map, affine minimal      112 372 385
Rational map, algebraic entropy      397
Rational map, algebraically integrable automorphism      430
Rational map, Arzel$\grave{a}$- Ascoli Theorem      25
Rational map, associated field extension      207
Rational map, associated Galois subgroup      207
Rational map, automorphism group      196
Rational map, automorphism group, $S_{3}$      197
Rational map, automorphism group, $\{z^{\pm 1}\}$      205 234
Rational map, automorphism group, contains $\mu_{2}$      235
Rational map, automorphism group, is finite      196
Rational map, automorphism group, of conjugate      196
Rational map, automorphism group, order two      235
Rational map, automorphism of order two      96 197 198 200
Rational map, backward orbit      109 142
Rational map, bad reduction      77
Rational map, bicritical      233
Rational map, Bogomolov conjecture      129
Rational map, can have infinitely many rational periodic points      136
Rational map, canonical height      99 287
Rational map, canonical height, lower bound      221
Rational map, canonical measure      127
Rational map, canonical measure, on Berkovich space      306
Rational map, cocycle gives twist?      203
Rational map, coefficients well-defined up to homogeneity      169
Rational map, commuting      378
Rational map, commuting, have same canonical height      137
Rational map, commuting, have same preperiodic points      38
Rational map, commuting, with polynomial      378
Rational map, completely invariant set      17
Rational map, completely invariant set, contains Berkovich Julia set      311
Rational map, condition for unequal formal and primitive periods      151 165 226
Rational map, conjugation is algebraic group action      173
Rational map, coordinate functions of iterate      149 226
Rational map, critical point      12 353
Rational map, critical point, distinct modulo $p$      237
Rational map, critical point, periodic      38
Rational map, critical value      353 382
Rational map, cutoff for integral points in orbit      375
Rational map, cyclic automorphism group      197 204
Rational map, defined at $P$      89
Rational map, degenerate quadratic      194
Rational map, degree      10 89 388 389
Rational map, degree generating function      397 428
Rational map, degree, of composition      392
Rational map, degree, of regular      394
Rational map, determined by $2d + 2$ coefficients      169
Rational map, domain of quasiperiodicity      310 311
Rational map, dynamical degree      397
Rational map, dynamical unit      71 72 79 132 133
Rational map, dynamical unit, of generic      146
Rational map, dynamically affine      376
Rational map, dynatomic field      123
Rational map, dynatomic polynomial      39 148 149 181
Rational map, dynatomic polynomial, is a polynomial      151 226
Rational map, effect on absolute value      288
Rational map, effect on height      90 388 398 409
Rational map, equi-Lipschitz family      313
Rational map, equicontinuous      22
Rational map, equicontinuous family      254 265 313
Rational map, even degree implies FOM = FOD      215
Rational map, expanding on average      36
Rational map, family omitting two points      265 315
Rational map, Fatou set      22 255
Rational map, field of definition      206 236
Rational map, field of moduli      177
Rational map, field of moduli, not field of definition      208 213 236
Rational map, finitely many preperiodic points      38
Rational map, finitely many with bounded height and resultant      237
Rational map, fixed point      149
Rational map, formal $n$-multiplier spectrum      182
Rational map, Galois equidistribution      128
Rational map, generalized dynatomic polynomial      227
Rational map, generalized period polynomial      227
Rational map, generic not very highly ramified      231
Rational map, global $S$-minimal model      237
Rational map, global minimal model      222
Rational map, global minimal model, over $\mathbb{Q}$      236
Rational map, global minimal resultant      220
Rational map, good reduction      58 59 218 239 362
Rational map, good reduction $\Rightarrow$ same degree      58
Rational map, good reduction, Berkovich Julia set      307 311 322
Rational map, graph      216
Rational map, Green function      288
Rational map, has $d + 1$ fixed points      149
Rational map, has $d^{n} + 1$ points of period $n$      150
Rational map, has $\nu_{d}(n)$ points of formal period $n$      150 224
Rational map, has nonrepelling fixed point      255 314
Rational map, has primitive periodic points of different periods      154 196
Rational map, height of      143
Rational map, height of, in $\mathcal{M}_{d}$      221 237
Rational map, Herman ring      28
Rational map, homogenization      389
Rational map, hyperbolic      279 285 317
Rational map, image of disk component may not be disk component      283
Rational map, indeterminacy locus      389
Rational map, induced      389
Rational map, induced map on disk components      283
Rational map, integer points in orbit      3 108 109 142 143
Rational map, integrality estimate for points in orbit      112 145
Rational map, invariant measure      127
Rational map, inverse function theorem      115 144 312
Rational map, involution      410 436
Rational map, is a morphism if...      89 388
Rational map, is continuous      10 24 253
Rational map, is open      10
Rational map, isospectral family      186 188 362
Rational map, iterate is a polynomial map      17 37 431
Rational map, iterates of open set omit at most one point      266
Rational map, iteration of regular is regular      394
Rational map, itinerary of a point      258 260
Rational map, Julia set      22 24 255 284
Rational map, lift of      389
Rational map, lift of, to affine space      287
Rational map, linear conjugation      11 173
Rational map, minimal model      220
Rational map, minimal resultant      237
Rational map, minimal resultant, is $PGL_{2}(K)$-invariant      221
Rational map, minimal resultant, of conjugate      219
Rational map, monomial      428
Rational map, Montel theorem      25 315
Rational map, most have no automorphisms      199 234
Rational map, most have no wildly critical point      284
Rational map, multiplier      18
Rational map, multiplier, at infinity      38
Rational map, multiplier, of fixed point      18 180
Rational map, multiplier, of periodic point      19 47
Rational map, multiplier, spectrum      182 187
Rational map, multiplier, summation formula      20 38 255 314 382
Rational map, new coordinate functions of conjugate      218
Rational map, no critical Julia points      279
Rational map, no twists if trivial automorphism group      198
Rational map, no wandering disk domains      284 285
Rational map, no wandering domains      28 276
Rational map, nonrepelling periodic point in Fatou set      256
Rational map, nonrepelling periodic points      64
Rational map, normal family      25
Rational map, normal form for degree two      190 233
Rational map, normalized form      51 75
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