# 2012$BG/EY(B $B5~ETNO3X7O%;%_%J!<(B

## 2012 Kyoto Dynamical Systems seminar

$BF|(B $B;~(B:
$BKh=56bMK(B14$B;~(B00$BJ,$h$j(B from 14:00, every Friday $B>l(B $B=j(B: $B5~ETBg3XBg3X1!M}3X8&5f2J(B 6$B9f4[(B 6$B3,(B 609$B%;%_%J!<<<(B ($BCO?^(B$B!K(B Room 609 at Building no. 6, at Facalty of Science, Kyoto University (Map) $B$3$l$^$G$N(B Kyoto Dynamics Days ### Kyoto Dynamics Day 12 $BF|;~!'(B3$B7n(B24$BF|!JF|!K(B10:30$B!A(B16:40 (24 March, 2013) $B2q>l!'M}3X8&5f2J(B3$B9f4[(B110$B<<(B (Kyoto Univ., Building No. 3, Room 110)
$B9V1i Dimitry Turaev $B;a!J(BImperial College London)
$B $B%W%m%0%i%$J$I$N>\:Y$ODI$C$F$*CN$i$;$7$^$9!%(B $B;~4V$K$D$$FOB?>/NJQ99N2DG=@-,"j^9!%(B ### Kyoto Dynamics Day 11 BF|;~!'(B2B7n(B18BF|!J7n!K(B10:30B!A(B16:40 (18 Feburuary, 2013) B2q>l!'M}3X8&5f2J(B3B9f4[(B108B<<(B (Kyoto Univ., Building No. 3, Room 108) B9V1i Lorenzo J. Diaz B;a!J(BPUC-Rio) B B%W%m%0%i%JIN>\:YO(B B3Ai(B Br4Mw/@5$$!%(B 19$BF|$K$O!$(BDiaz$B;a$K$h$k(Binformal seminar$B$r9T$&M=Dj$G$9!%(B

$B9V1i$N%?%$%H%k$H35MW!J?7$7$$=gKJBYF"j^9!K(B Titles and Abstracts • 2B7n(B8BF|!J6b!K(B B BJ?LL>eNNO3X7OK*1k(B antimonotonicity Abstract: BJ?LL>eNLL@QrJ]DNO3X7ON(B1B%Q%i%a!<%?B2N(B antimonotonicity BKD$$$F9M$($k!#(B Antimonotonicity $B$H$O!"$"$k%Q%i%a!<%?CM$N<~$j$G!"<~4|50F;$N@8@.!&>CLG$,$=$l$>$lL58B2s5/$3$k!"$H$$&8=>]G"k!#(B dissipative BJ(B saddle BK4X9k%[%b%/%j%K%C%/@\?(r;}D>l9gKO!"(BKan, Yorke BiKhCF8&5f5lF$$$k!#(B $B:#2s$O!"LL@Q$rJ]$DNO3X7O$G!"(Bantimonotone $B$K$J$kNO3X7O$N(B1$B%Q%i%a!<%?B2$NNc$r>R2p$9$k!#(B • 1$B7n(B25$BF|!J6b!K(B 15:00 $B$h$j(B
$B $B0l72:nMQ$N6K>.@-$HItJ,AP6J7?NO3X7O(B
Abstract:
$BItJ,AP6J7?NO3X7O$H8F$P$l$kHsAP6J7?NO3X7O$N%/%i%9$,$"$k!#(B $B$=$N$h$&$JNO3X7O$NNc$r9=@.$9$kJ}K!$H$7$F!"(Bskew-product $B$r(B $B$H$kJ}K!$,CN$i$l$F$$k!#(Bskew-product BN:nMQr(B B%U%!%%P!72:nMQ,F@ilk!#(B B6aG/!";dOItJ,AP6J7?NO3X7OrM}2r9k!V*bAc!WH7F(B BH>72:nMQN6K>.@-KD$$$F6=L#$r;}$C$F$$k!#(B B:#2sN%;%_%J!<GO!">eK5s2?;0BP>]N4X78!"(B B=7FH>72:nMQN6K>.@-K4X9k:G6aN7k2LKD$$$FOC$9!#(B $B;29MJ88%(B: On the minimality of semigroup actions on the interval which are C^1-close to the identity (arXiv:1210.0112)

• 1$B7n(B18$BF|!J6b!K(B NLPDE$B!&NO3X7O9gF1%;%_%J!<(B 15:00 $B$h$j(B
Yancong Xu $B;a(B (Department of Mathematics, Hangzhou Normal University, China) Snakes and isolas in non-reversible conservative systems Abstract: Reversible variational partial differential equations such as the SwiftHohenberg equation can admit localized stationary roll structures whose solution branches are bounded in parameter space but unbounded in function space, with the width of the roll plateaus increasing without bound along the branch: this scenario is commonly referred to as snaking. In this work, the structure of the bifurcation diagrams of localized rolls is investigated for variational but non-reversible systems, and conditions are derived that guarantee snaking or result in diagrams that either consist entirely of isolas. • 12$B7n(B21$BF|!J6b!K(B $BG_Ln(B $B7r(B $B;a(B ($B5~ETBg3X(B) $B7W;;$HDL?.$K$*$1$k%+%*%9Aj4X8z2L(B Abstract: $B!!6aG/!"7hDjO@E*%+%*%9$r:GE,2=7W;;!"%b%s%F%+%k%m7W;;!"DL?.MQId9f$KMQ$$?>l9gK!"2?Ey+N%Q%U%)!<%^%s%98~>e,F@ilkH$$$&Js9p$,$J$5$l$F$-$?!#(B $B9V1ie$,!"!I%+%*%9Aj4X!I$K$h$k8z2L$H$7$FE}0lE*$KM}2r$G$-$k$3$H$r<($7$?!#(B $B6qBNE*$K$O!"(B"$B%+%*%9Id9f(B"$B$r!"%(%k%4!<%IM}O@$K$h$k%k%Y!<%0%9%Z%/%H%kD>8r4pDl$K$h$j9=@.$7!"HFMQ%b%s%F%+%k%m7W;;$N(BSuperefficiency$B8z2L!"%9%Z%/%H%k3H;6DL?.!JL5@~DL?.!"EENO@~DL?.!K$X$N1~MQ!J(BCapacity Gain)$B$K$D$$F5DO@9k!#!!(B • 11B7n(B16BF|!J6b!K(B BM{(B BZ|N6(B B;a(B (BEl5~Bg3X(B) Entropy-expansive homoclinic classes: from ROBUSTLY to R-ROBUSTLY Abstract: Entropy-expansiveness is a kind of generalization of uniform hyperbolicity from the point of view of topological entropy. Due to a previous theorem by Pacifico and Vieitez (2010), robust sharing of this property can give some differential information in an open and dense subset of diffeomorphims nearby. In this talk, I would like to extend this theorem by introducing a relatively weaker assumption, called R- robustly entropy-expansiveness, which implies completely the same results as above. Moreover, some relevant ergodic consequences of index-adapted dominated splitting are provided. • 11B7n(B9BF|!J6b!K(B B:;@n(B B5.Bg(B B;a(B (B5~Bg(B) Second Law of Thermodynamics with Information Processing Abstract: The second law of thermodynamics is one of the most fundamental laws in physics, which quantitatively characterizes the irreversibility of the arrow of time. Since 1970B!G(Bs, theoretical and mathematical physiciss have investigated the theoretical foundation of the second law on the basis of the Shannon and von Neumann entropies. In this seminar, I'd like to talk about our recent theoretical results on generalizations of the second law of thermodynamics to information processing processes such as measurement and feedback, in which the mutual information and its quantum extension play crucial roles. I will also discuss the resolution of the paradox of B!H(BMaxwellB!G(Bdemo on the basis of our theoretical results. • 10B7n(B26BF|!J6b!K(B B9b66(B BGn Multifractal analysis for the Henon map at the first bifurcation Abstract: We study dynamics of the strongly dissipative Henon map at the first bifurcation parameter where the uniform hyperbolicityis destroyed by the formation of tangencies inside the limit set. We effect a multifractal formalism, i.e. decompose the phase space into level sets of time averages of a continuous function, and give partial descriptions of the Birkhoff spectrum which encodes this decomposition. Using a canonical induced map, we derive a formula for the Hausdorff dimension of the level sets in terms of Lyapunov exponent and entropy of invariant probability measures, and then show that the spectrum is continuous. The main idea is to relate each level set to embedded hyperbolic sets. References: [1] Y. M. Chung and H. Takahasi: Multifractal formalism for Benedicks-Carleson quadratic maps. Ergodic Theory and Dynamical Systems, to appear [2] S. Senti and H. Takahasi: Equilibrium measures for the Henon mapat the first bifurcation. (arXiv:1209.2224) [3] S. Senti and H. Takahasi: Equilibrium measures for the Henon map at the first bifurcation: uniqueness and geometric/statistical properties. (arXiv:1110.0601) [4] H. Takahasi: Prevalent dynamics at the first bifurcation of Henon-like families. Communications in Mathematical Physics (2012) 312, 37-85. • 10B7n(B19BF|!J6b!K(B B6b(B B1Q;R(B B;a(B (BBg:eBg3X(B) The minimal entropies of pseudo-Anosovs and the magic 3-manifold Abstract: B6JLL(B S Br8GDj9kH(B, S B>eN5<%"%N%=%U.CM(B l(S) Br;}D(B. B:G>.%(%s%H%m%T!<(B l(S) B,7hDj5lF$$$k6JLL(B S $B$NNc$O?t>/$J$$,(B, B3Nh&J6JLL(BSBK*$$$F(B, $B:G>.%(%s%H%m%T!<(Bl(S) $B$r.$5$J%(%s%H%m%T!<$r;}$D5<%"%N%=%U$,(B, $B$J$<(B, $B%^%8%C%/B?MMBN$+$i@8$^$l$k$N$+(B? $B$H$$&5?LdKD$$$F9M;!$7$?$$(B. • 10B7n(B12BF|!J6b!K(B B B@FZL@(B Abstract: B%O%_%k%H%s7ON2D@QJ,@-rH=Dj9k3HOD9$$4V8&5f$5$l$F$-$?=EMW$JLdBj$G$"$k(B. $B$=$NCf$G@FDj$N2<$GHs2D@QJ,@-$,>ZL@$5$l$k$h$&$K$J$C$F$-$?(B. $B$3$l$i$NM}O@$G$O(B, $BFC0[E@$r;}$D2r$N2r@O@\B3@-$d%b%N%I%m%_!<72$N9=B$$rK\eN0BDj(B/BIT0BDjB?MMBNN9=B$$+$i(B, $BHs2D@QJ,@-$r>ZL@$9$k(B.

• 7$B7n(B13$BF|!J6b!K(B
Davoud Cheraghi $B;a(B (University of Warwick) Trajectories of complex quadratic polynomials with an irrationally indifferent fixed point Abstract: The local, semi-local, and global dynamics of the complex quadratic polynomials$P_\alpha(z):=e^{2\pi i \alpha}z+z^2: \mathbb{C}\to \mathbb{C}$, for irrational values of$\alpha$, have been extensively studied through various methods. The main source of difficulty is the interplay between the tangential movement created by the fixed point and the radial movement caused by the critical point. This naturally brings the arithmetic nature of$\alpha$into play. Using a renormalization technique developed by H. Inou and M. Shishikura, we analyze this interaction, and in particular, describe the topological behavior of the orbit of typical points under these maps. • 7$B7n(B6$BF|!J6b!K(B $BJ?=P(B $B9L0l(B $B;a(B ($B0&I2Bg3X(B) The Cr interior and Cr boundary of the set of positively expansive Cr maps Abstract: $BJD%j!<%^%sB?MMBN>e$N(Bpositively expansive Cr maps $B$N=89g$N(B Cr $B0LAj$K4X$9$kFbIt$H6-3&$K$D$$F=RYk!#(B • 6B7n(B29BF|!J6b!K(B Carlos Cabrera B;a(B (UNAM, Mexico) Semigroups in holomorphic dynamics Abstract: We use semigroup theory to describe the group of automorphisms of some semigroups of interest in holomorphic dynamical systems. The main tool for our discussion is a theorem due to Schreier. Finally, we show that under an algebraic condition the Fatou-Sullivan conjecture holds. • 6B7n(B22BF|!J6b!K(B B;32<(B BLw(B B;a(B (BF`NI=w;RBg3X(B) Out(F_n) actions on character variety Abstract: Let Hom(F_n, SL(2,C)) be the set of representations from the free group of rank n to SL(2,C). SL(2,C) acts on this representation space by post-composition of conjugation and the quotient space Hom(F_n, SL(2,C))/SL(2,C) is called SL(2,C)-character variety. The outer-automorphism group Out(F_n) acts on this quotient space. In this talk, we investigate the dynamics of this action and show some computer generated pictures. • 6B7n(B15BF|!J6b!K(B Laura DeMarco B;a(B (University of Illinois at Chicago) Special curves and post-critically-finite polynomials Abstract: In a joint project with Matt Baker, we study algebraic curves in the moduli space of polynomials. We are interested in a characterization of curves that contain infinitely many post-critically-finite (PCF) maps. Our general conjecture may be described as a dynamical analog of the Andre-Oort conjecture in arithmetic geometry. The proof (of the cases we can handle) involves a combination of (1) arithmetic equidistribution theorems and (2) classical complex analysis and dynamics. I will make the talk accessible to graduate students. The first part will be an overview of the question and historical context, with examples and an outline of the proof. • 6B7n(B1BF|!J6b!K(B BFA1J(B BM52p(B B;a(B (BBg:eBg3X(B) Measures with maximum total exponent of diffeomorphisms with basic sets Abstract: B%3%s%Q%/%H(BRiemannianBB?MMBN>eNHyJ,F1Aj • basic setB>eN:GBgA4;X?tB,EYOM#0lDB8:_9k!#(B • basic setB>eNG0UN:GBgA4;X?tB,EYK4X7FNB,EYO@E*%(%s%H%m%T!<O(B0BG"k!#(B • basic setB>eNG0UN:GBgA4;X?tB,EYNBfO(Bbasic setBH0lCW9k!#(B B^?!"(BC1B5ihj6/$$@5B'@-$r$b$DHyJ,F1Ajl9g$HBg$-$/0[$J$k$3$H(B $B$r<($9!#(B

• 5$B7n(B18$BF|!J6b!K(B
Johannes Jaerisch $B;a(B ($BBg:eBg3X(B)
Amenability and Recurrence of Normal Subgroups of Kleinian Groups from a Thermodynamical Viewpoint
Abstract:
We show that some results on normal subgroups of Kleinian groups have their natural home in the thermodynamic formalism of Markov shifts with a countable state space. This includes a result of Brooks which states under certain conditions, that for a normal subgroup N of Kleinian group G, we have that \delta(N)=\delta(G) if and only if G/N is amenable, where \delta refers to the exponent of convergence of the associated Poincare series. Another result, which is due to Falk and Stratmann and to Roblin, shows that \delta(N) is bounded below by half of \delta(G) and that this inequality is strict whenever G is of divergence type. We give a short new proof of this result.

• 5$B7n(B11$BF|!J6b!K(B ($B0JA0M=Dj$7$F$$?(B Qiudong Wang B;aN9V1iO%-%c%s%;%kKJj^7?(B. ) B2#;3(B BCNO:(B B;a(B (BKL3F;Bg3X(B) Recurrence, pointwise almost periodicity and orbit closure relation for flows and foliations Abstract: B%3%s%Q%/%HJ6JLL>eN%Y%/%H%k>lKD$$$F!$(B $B0J2<$N;0$D$,F1CM$K$J$k;v$H!$$=N>ZL@%-!<HJk%"%%G%"r=RY^9(B: pointwise recurrentB!(Bpointwise almost periodic."minimal or pointwise periodic". B5iK!(Bdivergence-freeB!6JLL>eNF1Aj • 4B7n(B20BF|!J6b!K(B B>eLn(B B9/J?(B B;a(B (BD;1)>&A%9b@l(B) Green functions and weights of polynomial skew products on C^2 Abstract: We study the dynamics of polynomial skew products on C^2. By using suitable weights, we prove the existence of several types of Green functions. Largely, continuity and plurisubharmonicity follow. Moreover, it relates to the dynamics of the rational extensions to weighted projective spaces. • 4B7n(B13BF|!J6b!K(B NLPDEB!&NO3X7O9gF1%;%_%J!<(B 15:30 Bhj(B BM}3X8&5f2J(B3B9f4[(B108B9f<<KF(B B@iMU(B B0o?M(B B;a!J6e=#Bg3X!K(B B0lHL2=%9%Z%/%H%kM}O@H=NL58B Abstract: Gelfand tripletBH8FPlk!"@~7A0LAj6u4VN#3DAH>eGN@~7A:nMQAGN(B B%9%Z%/%H%kM}O@rE83+9k!#DL>o!":nMQAGN%9%Z%/%H%kO!"(BCB>eK*1k(B B%l%>%k%Y%s%HNFC0[E@=89gH7FDj5A5lk,!"(BGelfand tripletBrF3F~9kH!"(B B%l%>%k%Y%s%H,J#;(J(BRiemannBLLr;}A&k!#=3G!"(BRiemannBLLA4BNr(B B8+EO7?;~N%l%>%k%Y%s%HNFC0[E@=89gr0lHL2=%9%Z%/%H%kH8FV!#(B B0lHL2=%9%Z%/%H%kO!"IaDLN%9%Z%/%H%kHF18/i$$!":nMQAG$K$D$$FN(B B=EMWJ>pJsr;}CF*j!"3lrMQ$$$k$3$H$G=>Mh$O8+$($J$+$C$?8=>]$r(B $BB*$($k$3$H$,$G$-$k!#(B $B9V1i$G$O!"$3$l$r$/$D$+$NL58B $BO"Mm@h!'(B

$B@u2,(B $B@59,(B (asaokaQmath.kyoto-u.ac.jp, replace Q with at-mark)
$B")(B606-8502 $B5~ET;T:85~6hKLGr@nDIJ,D.(B
$B5~ETBg3XBg3X1!M}3X8&5f2J(B $B?t3X65<<(B