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

Orbit      1
Orbit, -integral points in      143
Orbit, backward is dense in Julia set      267
Orbit, finite iff canonical height zero      423 431
Orbit, Galois-invariant on K3 surface      436
Orbit, height zeta function      436
Orbit, integral points      3 108 109 142 143
Orbit, integral points, construction of many      110 111 143 375
Orbit, integral points, cutoff for      375
Orbit, integral points, uniform bound for      112 372 385
Orbit, integrality estimate for points in      112 145
Orbit, number over a finite field      430
Orbit, of critical points      280
Orbit, of critical points, is bounded      26 165
Orbit, of critical points, is unbounded      26
Orbit, of Galois conjugate      137
Orbit, of open set omits at most one point      266
Orbit, product of multipliers      19
Orbit, two sided      432
Orbit, under collection of rational maps      143
Orbit, Zariski dense on K3 surface      435
Orbit-counting function      432
Order, in quadratic imaginary field      341
Order, in quaternion algebra      341
Order, of a holomorphic function      244
Order, of a meromorphic function      244
Ostrowski’s theorem      44 312
Parabolic component      28
Path metric      306 323
Path metric, does not induce Gel’fond topology      323
Path-connected      304
Path-connected, Berkovich disk is      300
Path-connected, same as disk-connected over $\mathbb{C}$       277
Pell equation      106
Perfect set, Berkovich Julia set is      307 311
Perfect set, Julia set is      267
Period polynomial      149 181
Period polynomial, dehomogenized      149
Period polynomial, for $z^{2} + c$       156
Period polynomial, generalized      227
Period polynomial, homogeneous of degree $d^{n} + 1$       181
Period polynomial, multiple root      230
Period polynomial, order at $P (a_{p}(n))$       151
Period, exact      150
Period, formal      150
Period, of a point      1
Period, primitive      150
Periodic disk component      283
Periodic domain      28
Periodic point      1
Periodic point, -adic      361
Periodic point, -adic distance      69
Periodic point, algebraic family induces map to dynatomic curve      159
Periodic point, algebraic family of with given formal period      159
Periodic point, algebraic properties      3
Periodic point, attracting      19 326 362
Periodic point, attracting, for good separable reduction      64
Periodic point, attracting, iff reduction is critical      78
Periodic point, attracting, in Berkovich space      310
Periodic point, attracting, in Fatou set      22
Periodic point, basin of attraction      310
Periodic point, canonical height zero      99
Periodic point, Chebyshev polynomial      41
Periodic point, closure contains Julia set      273
Periodic point, closure of repelling equals Julia set      274
Periodic point, condition for unequal formal and primitive periods      151 165 226
Periodic point, critical      38
Periodic point, critical point with reduction a      78
Periodic point, cycle of      150
Periodic point, cyclotomic      95
Periodic point, dense for shift map      314
Periodic point, differential one-form definition of multiplier      19
Periodic point, discrete      428
Periodic point, dynamical unit      69 71 72 79 132 133
Periodic point, dynamics on finite set      7
Periodic point, dynatomic field      123
Periodic point, equation of      122
Periodic point, equidistribution      6
Periodic point, every is attracting      78
Periodic point, exact period      18 38 150
Periodic point, field generated by      122
Periodic point, finitely many on K3 surface      435
Periodic point, finitely many rational      8
Periodic point, finiteness for regular affine automorphism      400
Periodic point, finiteness over       3
Periodic point, finiteness over number field      66 94 407
Periodic point, flexible Latt $\grave{e}$ s map      358 382
Periodic point, form subgroup      8
Periodic point, formal period      18 39 150
Periodic point, formal period, moduli problem      158
Periodic point, Galois theory of field generated by      122
Periodic point, generalized dynatomic polynomial      227
Periodic point, generalized period polynomial      227
Periodic point, immediate basin of attraction      310
Periodic point, index summation formula      20 38 382
Periodic point, indifferent      19 326
Periodic point, irrationally neutral      19 47
Periodic point, isolated      402
Periodic point, Julia set is closure of nonrepelling      27
Periodic point, Latt $\grave{e}$ s map      186
Periodic point, least period      18
Periodic point, multiplier      18 19 47
Periodic point, multiplier, at infinity      38
Periodic point, multiplier, Latt $\grave{e}$ s map      35 186
Periodic point, multiplier, of critical      38
Periodic point, multiplier, power map      326
Periodic point, nonrepelling      362
Periodic point, nonrepelling, for good reduction      64
Periodic point, nonrepelling, in Fatou set      256
Periodic point, number of      39
Periodic point, number of, given period      122
Periodic point, number of, nonrepelling cycles      27
Periodic point, of $(z^{2} - z)/p$       263
Periodic point, of $z\cdot\cdot\cdot(z - d + 1 )/p$       315
Periodic point, of $z^{2} + 1$       8
Periodic point, of $z^{2} - 1$       8
Periodic point, of $z^{d} + a$ over finite field      8
Periodic point, of commuting maps      8 378
Periodic point, of power map      326
Periodic point, of quadratic polynomial map      96
Periodic point, of regular affine automorphism      394
Periodic point, on subvariety      127
Periodic point, one indifferent implies infinitely many      314
Periodic point, prime period      18
Periodic point, primitive      122
Periodic point, primitive period      18 150
Periodic point, primitive, field generated by      123
Periodic point, product of multipliers in orbit      19 47
Periodic point, rational map can have infinitely many rational      136
Periodic point, rational map has points of different periods      154 155 196
Periodic point, rationally neutral      19
Periodic point, rationally neutral, in hyperbolic component      28
Periodic point, reduction of      61 62 66 78
Periodic point, regular affine automorphism      400
Periodic point, relative abelian extension      126
Periodic point, repelling      19 47 326 361
Periodic point, repelling in Julia set      256
Periodic point, repelling, in Berkovich space      310
Periodic point, repelling, in Julia set      22
Periodic point, repelling, limit of attracting      274
Periodic point, residual degree      310
Periodic point, rigid Latt $\grave{e}$ s map      366 384
Periodic point, set of is Galois-invariant      123
Periodic point, shift map      259
Periodic point, summation formula      20 38 255 314 380 382
Periodic point, superattracting      19 47
Periodic point, Type — I      310
Periodic point, Type — II      310
Periodic point, Type — IV      321
Periodic point, uniform boundedness conjecture      96 135 368

Periodic point, uniform boundedness conjecture, for $z^{d}$       137
Periodic point, uniform boundedness conjecture, for Latt $\grave{e}$ s map      370
Periodic subvariety      127
Permutation group      124
Permutation polynomial      5
Picard group      339 403
Picard group, action of involution      418 438
Picard group, degree map      405
Picard group, eigenvalue of involution      421
Picard group, exact sequence      404
Picard group, generated by hyperplane      405
Picard group, height map on      408
Picard group, intersection theory for K3 surface      434
Picard group, isomorphic to elliptic curve      339
Picard group, linear transform induced by involution      420
Picard group, of $\mathbb{P}^{2}\time\mathbb{P}^{2}$       418
Picard group, of $\mathbb{P}^{N}\time\mathbb{P}^{M}$       405 409
Picard group, of general K3 surface      418
Picard group, pullback homomorphism      405
Point, absolute value      90 288
Point, at infinity      10 11
Point, at infinity, on elliptic curve      336
Point, field of definition      86 122
Point, polynomial action on Berkovich      305
Point, radius of in Berkovich space      296
Point, reduction modulo a prime      48
Point, sup norm      90 288
Pole      244
Polynomial map      17
Polynomial map, cannot have Herman ring      28
Polynomial map, canonical measure on Berkovich space      306
Polynomial map, Chebyshev      29 95 329
Polynomial map, Chebyshev, in characteristic       381
Polynomial map, commuting      378
Polynomial map, complete invariance of component at infinity      40
Polynomial map, condition for unequal formal and primitive periods      165
Polynomial map, cyclotomic preperiodic points      95
Polynomial map, dynamical unit      71 132
Polynomial map, dynamical unit, of generic monic      146
Polynomial map, effect on absolute value      288
Polynomial map, filled Julia set      74 140
Polynomial map, finitely many rational periodic points      8
Polynomial map, fixes Gauss point      321
Polynomial map, FOM = FOD      215
Polynomial map, good reduction      321 322
Polynomial map, has primitive periodic points of different periods      155
Polynomial map, iff $\sigma_{1}(\phi) = 2$       232
Polynomial map, iterate is a      17 37
Polynomial map, iterates of open set omit at most one point      266
Polynomial map, Latt $\grave{e}$ s map not conjugate to      381
Polynomial map, local canonical height      103 141
Polynomial map, monomial      29 95 325
Polynomial map, multipliers not equal to one      41
Polynomial map, nontrivial automorphism group      234
Polynomial map, number of nonrepelling periodic cycles      27
Polynomial map, on Berkovich space      304
Polynomial map, power      95
Polynomial map, power map      29 321 325
Polynomial map, power map, in characteristic       380
Polynomial map, power map, on Berkovich space      321
Polynomial map, radius of image disk      321
Polynomial map, sends disks to disks      305 312
Polynomial map, wandering disk domains exist over $\mathbb{C}_{p}$       286
Polynomial type rational map      143
Polynomial, $ord_{p}$       218
Polynomial, absolute value of      91
Polynomial, bidegree      405
Polynomial, bihomogeneous      405
Polynomial, bounded seminorm on ring of      296
Polynomial, cyclotomic      148 224
Polynomial, degree of      389
Polynomial, dynatomic      148 149 181
Polynomial, elementary symmetric      87
Polynomial, Gauss norm      296
Polynomial, height of roots      136 138
Polynomial, homogeneous      10
Polynomial, homogeneous ideal      89
Polynomial, local canonical height      140
Polynomial, normalized      51
Polynomial, number of monomials      136
Polynomial, permutation      5
Polynomial, resultant of two      53
Polynomial, sup norm      91 288
Polynomial, trihomogeneous      437
Positive divisor      see effective divisor
Positivity of height      408
Postcritical set      280 353
Potential good reduction      371
Potential theory on Berkovich space      323
Potential theory on Berkovich space, Hsia kernel      323
Power map      29 325
Power map, automorphism group      234 327
Power map, automorphism group, in characteristic       380
Power map, commuting maps      326 378 380
Power map, dynamical unit      328
Power map, in characteristic       380
Power map, multiplier of periodic point      326
Power map, on Berkovich space      321
Power map, periodic point      326
Power map, preperiodic point      326
Power map, twist      206 328 380
Power series      244
Power series, coefficients uniquely determined by function      312
Power series, converges iff $a_{n}\rightarrow 0$       244
Power series, distance between image disks      268
Power series, family omitting one point      264 315
Power series, formal      5
Power series, maximum modulus principle      250
Power series, Montel theorem      264 271 315
Power series, Newton polygon      249
Power series, norm of derivative      252 313
Power series, periodic points in ring of      78
Power series, product of      312
Power series, sends disks to disks      252 305
Power series, Tate algebra      297
Preperiodic disk component      283
Preperiodic disk domain      284 285
Preperiodic domain      28
Preperiodic point      1
Preperiodic point, canonical height zero      99
Preperiodic point, critical      26
Preperiodic point, cyclotomic      95
Preperiodic point, dynamics on finite set      8
Preperiodic point, finitely many      38
Preperiodic point, finiteness over number field      94 407
Preperiodic point, Galois equidistribution      128
Preperiodic point, generalized dynatomic polynomial      227 229
Preperiodic point, generalized period polynomial      227
Preperiodic point, isolated      8
Preperiodic point, large ramification index implies is      37
Preperiodic point, Latt $\grave{e}$ s map      32 352
Preperiodic point, of abelian group is torsion      2 41 326
Preperiodic point, of commuting maps      8 38 378
Preperiodic point, of multiplicative group      326
Preperiodic point, of power map      326
Preperiodic point, on subvariety      127
Preperiodic point, reduction of      61
Preperiodic point, Type-lV      321
Preperiodic point, uniform boundedness conjecture      96 135
Preperiodic point, uniform boundedness conjecture, for $z^{d}$       137
Preperiodic point, uniform boundedness conjecture, for Latt $\grave{e}$ s map      370
Preperiodic subvariety      127 128
Prerequisites      7
Prime divisor      403
Prime divisor, degree      405
Prime divisor, local ring      403
Prime is sum of two squares      200 236
Prime period      see exact period
Primitive period      see exact period
Primitive periodic point      122

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